I have managed to "fix" most of the issues I have with the weapon table by making a few houserules. Those houserules generally add to weaker weapons, rather than weaken stronger weapons. For example, I created the Off-Hand property for several 1d4 light weapons that allow them to be used for TWF with any other weapon (making longsword and dagger viable). I added the Grapple trait to the Trident, allowing it to be used to for grappling and granting advantage to attack the grappled target (but can't attack anyone else until the grapple ends). I gave the Greataxe the Brutal (d12) property, which means it deals +1d12 on a critical hit (I KNOW it seems like a lot, but with the assumption of a die roll of 10 to hit, that appears to be the exact difference between the 1d12 and 2d6 weapons in damage over 20 attacks).
If I was going to do a full rewrite (which I would prefer), I think that a base mechanic table should be used. For example, have simple weapons deal 1d6 damage and martial weapons deal 1d8. Beneficial properties lower the damage, while restrictive ones raise it. Some weapons can (and should) be generally worse, mostly simple weapons used by primitives (club, greatclub, etc.), but most martial weapons should be fairly balanced because only martial trained characters would use them... and martial trained characters likely aren't going to use crap.
My major things:
1) Make Versatile a variable property. Some weapons might get an attack bonus, some a damage bonus, or some other benefit suitable for the weapon. For example, the spear could be a martial weapon, but only a simple weapon when used two handed. The longsword could grant +1 attack when used 2 handed, but the battleaxe deals +2 damage instead, giving each a different purpose.
2) Similar weapons could be combined into single weapons, but the description include the ohters. Right now the longsword represents the longsword, broadsword, and bastard sword. The scimitar has traditionally included the cutlass and sabre in prior editions. The halberd and glaive are identical mechanically, as would be a bunch of similar slashing polearms, so listing them as a single weapon would be good. Ditto for piercing polearms. By including these weapons in the descriptions, this allows players to have a variety of weapons without flooding the table mechanics with a million options (as Gygax did with polearms in 1E).
3) Fighting Styles should have been weapon based, not generic. They tried to correct this with feats in one of the UA, but it was iffy. In addition to not helping games that don't use feats, it almost becomes a feat tax to differentiate your weapon choice.
Two minor things:
1) The crossbow should not have a modifier to damage, since it's the mechanics that cause the damage. It should deal straight dice that are higher than other weapons to compensate. In addition, they should all be simple weapons; crossbowmen were easy to train, good bowmen were hard to come by.
2) The pike is ridiculous as a character weapon choice. It was never intended to be used alone, only with a line of other pikemen. It would have extra reach (15'), but be useless up close (5'). I wouldn't object to a longspear polearm to take its place mechanically, but the pike isn't a weapon that should be used in a skirmish, which is what D&D is based around.
