This initiative System which you are considering to add more "reality" to your game is B(ad)S(olution). Sorry for my strong language, no offense but i get a bit tired to point out again and again that long/two handed weapons have far more velocity (because of weapon edge sitting on a longer Lever) and are attacking first in a RL Scenario because they have REACH.
So if you are adding modifiers to initiative it goes from this fastest to slowest:
Cocked crossbow
Bow
sling
Pike / Lance
Spear polearm quarterstaff
Two handed sword /axe greatclub / rapier (Rapier because of its insane reach, not because it is light in reality, in fact it weighs as much as a longsword)
Longsword
Mace battleaxe etc
Hand axe dagger etc Yes your dagger fighter will get attacked and hit before he get's into the reach which allows him to apply his own weapon!
Especially in your System consider this two points:
you give dexterity stat even more overpower than it already has, because it already determines base initiative
The forfeiting the Action is an as heavy toll as can be since in 5e most fighsts are only Lasting 1-4 rounds, to sit out one of these rounds without an enemy spending a resource, because of some houserule is far to much and might break game Balance.
Somewhat agree but would note:
Weapon length does give leverage, but the longer weapon also has more mass. A claymore wielded one handed is not faster than a rapier or longsword wielded one handed. The second hand is what gives you the greater leverage (more impetus to the swing).
Most D&D weapons (at least back in the AD&D days, haven't checked the 5E tables) were far overweight for the sorts of swords people fought with. The Italians did a *lot* of sword fighting through some periods of their history and the most common sword was the smallsword (and it is quite light). Their longer blades were still very light compared to what D&D claimed (I think an original longsword was 4 pounds and a 2 hander 15 pounds). Those game weights were not terribly accurate - Anything over about 3 pounds is not going to be something you can swing for very long even with strong arms in a fight. Yes, I imagine the hand-and-a-half and two handers passed that weight, but they just weren't wielded with the speed you'd want for a sword clash - two handers were either for big chops at unarmoured targets or were for chopping the heads of of pikes or the like, not for the to-and-fro of an actual sword duel.
So it's even more opaque than we usually think.
Also, many of the swords people have used as historical examples were display pieces (which is why some of the weights and notions of use were fairly incorrect, much like peoples' ideas of how hard it was to move in heavy armour like plate and mail or how short or slight knights were (based on finding a few sets of armour that suggested occupants were 5'6" with a very small waist)).
It's a pretty simple test if you are in good shape and have strong arm muscles. Put a 1 pound or 3 pound weight in your hand and swing it back and forth fairly rapidly and see how many minutes you can keep that up before you get a lot slower. I'm fairly sure for most people in good shape, that's still on the order of a minute or less if you swing vigorously and vary your swings.
Your point about adding additional potence to dexterity is also well called-out.
Plus one thing not modeled explicitly is the combat style used: Some weapons and some unarmed moves are *not initiated* but are planned reactions to enemy attacks. Aikido and most other soft arts and a few of the schools of classial sword fighting had moves that were 'he stabs, you turn away or step off, grapple his arm (or cut it with your knife)'. So in this case, you are accepting the fact you may have a shorter weapon, but he has to stick a limb out to get at you and at that point, you can counter (if you are not impaled on his sword). In fact, arnis/escrima is based on the notions of 'first in' (strike first) and 'if he gives you a limb, break it... once he has no limbs, the fight is over'. They basically can wait for an attack and then attack the limb with sticks, butterfly knives, or unarmed.