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Let's examine the first issue, as the second will become evident as we realize the questions that evolve from using weapon speeds in D&D.
Realistically, because a dagger is a smaller weapon, a person should be able to attack with it more quickly and more often than someone using a larger weapon, simply because a smaller weapon has less mass and therefore less inertia -- it's easier to move it about than a larger weapon. However, the larger weapon has an advantage over the smaller weapon - reach. Laral the Longsword is going to be able to hit a Darvin the Dagger before Darvin can get close enough to strike at Laral. So these tend to cancel out, and weapon speed isn't a factor because we default to a 5-foot reach in D&D. Introducing weapon speed implies a level of precision that would require the rules to be adjusted to take into account reach in increments other than 5 feet. That's a lot of work, and it would make the game much more complex (slowing down combat greatly, which is a bad thing if you're trying to get something done in a night other than a simple CR-appropriate encounter).
Let's assume that they don't cancel out and proceed with the argument.
Everyone says that daggers should have a faster speed factor than a longsword because a dagger can be swung faster than a longsword. But what does that "can be swung faster" mean in D&D? Let's take a 5th-level fighter as an example. A 5th-level fighter is someone that is reasonably skilled with a weapon, but not so skilled that they get an iterative attack (base attack bonus has not yet reached +6/+1, in other words). Laral and Darvin are both 5th-level fighters with identical feats and stats. So let's take a look at the stats.
In 10 rounds of combat, without weapon speeds, Laral gets 10 attacks and Darvin gets 10 attacks. With weapon speeds (assuming it's some sort of initiative bonus or penalty), Laral gets 10 attacks and Darvin gets 10 attacks.
So including weapon speeds doesn't actually make Darvin attack faster (he's getting the same number of attacks).
So why have weapon speeds? If it's supposed to reflect that you can strike faster with the weapon, but implementing a bonus or penalty to initiative doesn't do that, why do it?
Flat Initiative Modifiers
Ignoring that excellent point, let's assume that your weapon speeds are a simple bonus or penalty to initiative. So (because higher initiative is better, a faster weapon has to give you a better initiative plus) let's say a dagger would be +4, a longsword would be +0 (assuming it's the "standard"), a battleaxe would be -2, and a hammer would be +1. Therefore, if Darvin and Laral were in combat with Argresh the Axe and Henril the Hammer, they might roll the following on the d20 for initiative (assuming none have an initiative bonus):
With the weapon speeds included, their initiatives become (after sorting highest to lowest)
So, this seems all straightforward. Darvin's going to get to attack before anybody. Let's skip on to round 2 and confuse the issue a bit.
On Darvin's turn, he drops his dagger and draws his battleaxe. Should he still in 17, or is his new initiative 13 (the original roll) -2 (battleaxe modifier) = 11? Is he suddenly going after Laral (initiative 12) in combat? On this round does he get to attack in 17, or does he in effect have an automatic Delay action which forces him to wait until 11 to attack? Or does he act normally on his turn, and next turn uses the new initiative number?
It's even weirder if Argresh drops his axe and draws a dagger. Suddenly his initiative score goes up to 15. Does the DM have to retrofit his actions into earlier parts of the combat, before Laral and Henril, since his initiative is higher? Or does it take effect only on the next round?
And what if you have two weapons? Do you add the modifiers together? That makes the two-dagger fighter way too fast and the two-axe fighter way two slow. Do you take the higest one? That means that anyone with an axe would be smart to have a dagger in the other hand, just in case and just to get the +4 initiative modifier for having the faster weapon.
This variant system would also require the heroes to remember multiple initiative numbers - their original one and the one modified by their current weapon. More record-keeping slows down the game.
Oh, and you'd have to come up with casting times (initiative modifiers) for each spell in the game. And probably for spell-like and supernatural abilities, too.
Cumulative Initiative Penalties
One suggestion might be to give all weapons a penalty compared to an unarmed strike, and each round the characters modify their current modified initiative by whatever weapon they're holding (for example, if a dagger is -1, Darvin's initiative would go down by 1 every round). That way, everyone slides down the initiative ladder, people can switch weapons without going "back in time" to an earlier initiative, and those using fast weapons slide down slower than others. Compared to each other, the combatants stay relatively in synch, and it means that after ten rounds Darvin is certainly going "first" (whatever that means in cyclic initiative) compared to Argresh, even if Argresh somehow got the drop on Darvin in the first round (say, by beating his initiative roll by 20).
However, this introduces another problem: the characters become out of synch with the world. If after 10 rounds of combat all of the participants have slid down to 5 or below (and possibly into negative numbers, since that's perfectly okay in the D&D system), and new creature that enters the fray is going to go before them because it's not saddled with 10 rounds of weapon speed initiative penalties (it's using the standard 1d20 + bonuses since it has 0 rounds of penalties).
Sure, you could throw in some rules that say that if at the end of the round one or more characters have reached 0 initiative, you scale everyone upward again by the same amount so that the highest-initiative character is back at their original initiative roll. This would correct the above problem hat occurs when a new creature enters the fray. Unfortunately, this revision just means that Argresh the Axe continues to get worse and worse in initiative each round, and the gulf widens between him and Darvin, until eventually the DM has to "reset" the initiative every round (because Argresh is at initiative 1 and automatically triggers a reset at the end of the round with his slow weapon). Furthermore, Argresh may have initially rolled a 20 on his initiative, but after 10 rounds he's near 1, and just about any newcomer to the fight is going to be reacting before him, even though you've been "adjusting" the initiative to compensate for weapon speeds. You could have all of the characters reroll when a new creature enters the fight, but that means that suddenly Argresh might be going before Darvin ... which means that what Argresh really wants is a series of buddies to wait off-screen and enter combat every three rounds or so to give him a chance to reroll initiative. That's metagame thinking, and it's not good for gameplay.
Adjusting Iterative Attacks
Another option is to make faster weapons adjust the user's rate of iterative attacks. Thus, a character using a longsword that would only get 1 attack per round because of his BAB might get 2 attacks per round by using a dagger because instead of the standard -5 progression for iterative attacks, the dagger might give you a -4 progression. That same character using a glaive might not get iterative attacks with for several more levels because a glaive's iterative attacks are every 7 levels instead of every 5. If small weapons are supposed to be "faster," this is more realistic when viewed through the lens of the game mechanics because a dagger-user would get more attacks in 10 rounds than a longsword-user. At first glance, it appears better than the initiative-modifying system.
But it gets ugly quickly, because monk's unarmed BAB progression would need to be changed (since it should be even faster than a dagger), probably to every 3, and it would be a bear to properly balance variant iterative progressions for each weapon. It also would mean that for many levels, two weapons of different sizes wielded by users of similar skill would still have the exact same number of attacks per round.
For example, two 4th-level fighters would still only get one attack per round with a longsword (iterative -5) or dagger (iterative -4). That's not so bad, since they're still pretty low-level.
Those two fighters at level 5 would see a difference, because Laral would be attacking at +5 only, while Darvin would be attacking at +5/+1. Let's make a comparison between the two for levels 1-20:
("dagger +1" means the dagger-user is getting 1 more attack per round compared to the longsword-user)
So, even after going through all of these complex motions, the dagger fighter only gets an extra attack half the time (10 levels out of 20, compared to the longsword fighter ). The work necessary to make these variant iterative progressions balanced isn't worth the small reward for doing so. And you would have to rewrite the Improved Two-Weapon Fighting (since it gives an explicit -5 penalty on the off-hand weapon's attack, which doesn't reflect the speed of "faster" weapons).
And would these small, fast weapons have different iterative values for when you were using them in melee or in ranged?
And regardless of the above answer, if you had a +15 BAB (which would normally get you three attacks under the current D&D system), what would happen if you chose to throw two daggers (fast) and a throwing axe (not so fast)? They're going to have different iterative attack values, so you shouldn't just get one or the other.
Finally, you could always do something like what the speed weapon property does -- give you just one extra attack per round. The variable for weapon speed would be the penalty at which you made that extra attack. A fast weapon such as a dagger might allow you one attack per round at a -1, while a slower weapon like a short sword might allow you an extra attack at -5, and a longsword or slower weapon might not allow any extra attacks at all. Again, that's a lot of work to figure it out and make it balanced, in exchange for a very small benefit. Balance is a big issue; anyone can guess at numbers, but testing it to make sure that the guessed numbers don't give an unfair advantage to a weapon that shouldn't have it takes time and effort. I don't think it's worth the investment of either to get it done.
And the smaller weapons' speeds are canceled out by larger weapons' reach anyway. ;)