EzekielRaiden
Follower of the Way
It's an interesting notion, but it doesn't play super nicely with some of 5e's existing design. For example, there are effects that allow you to reroll or alter one weapon die, and these are much less useful for the already-existing 2d6 weapons than they are for the "equivalent" 1d12 weapons. Adding in dice of different sizes makes this even more complicated, because now there's a meaningful choice between (say) rerolling the d6 vs the d4.
That said, I do appreciate the idea of weapon properties and keywords; I truly wish 5e had kept more of 4e's weapon properties (like brutal, high crit, and stout), and doubly that they'd kept the [W] notation that would make your suggestion completely compatible with the rules. E.g. if an attack does "3[W]," it means you roll three rolls of your weapon's damage dice, no matter what those dice are. So a 2d6 weapon used with a 3[W] effect would roll 3[2d6] = 6d6 damage, while a 1d12 weapon used with that same effect would do 3[1d12] = 3d12 damage.
As a possible middle-ground, you could consider expanding the range of the "1dX" vs "2d(X/2)" options. E.g., it's easy to create d2, d3, and d5 dice by just halving any even roll from a d4, d6, and d10. That could then give us 2d2, 2d3, 2d4, and 2d5 weapons, none of which exist in 5e as it stands. They'd be more reliable but slightly less potent than their 1d4, 1d6, 1d8, and 1d10 cousins (e.g. a 2d5 weapon has about half the chance of rolling 10 as a 1d10 does, but it can't roll a 1 and is less than half as likely to roll a 2.) Checking around online, it sounds like a homebrew falchion as a 2d4 weapon is a moderately common thing.
That said, I do appreciate the idea of weapon properties and keywords; I truly wish 5e had kept more of 4e's weapon properties (like brutal, high crit, and stout), and doubly that they'd kept the [W] notation that would make your suggestion completely compatible with the rules. E.g. if an attack does "3[W]," it means you roll three rolls of your weapon's damage dice, no matter what those dice are. So a 2d6 weapon used with a 3[W] effect would roll 3[2d6] = 6d6 damage, while a 1d12 weapon used with that same effect would do 3[1d12] = 3d12 damage.
As a possible middle-ground, you could consider expanding the range of the "1dX" vs "2d(X/2)" options. E.g., it's easy to create d2, d3, and d5 dice by just halving any even roll from a d4, d6, and d10. That could then give us 2d2, 2d3, 2d4, and 2d5 weapons, none of which exist in 5e as it stands. They'd be more reliable but slightly less potent than their 1d4, 1d6, 1d8, and 1d10 cousins (e.g. a 2d5 weapon has about half the chance of rolling 10 as a 1d10 does, but it can't roll a 1 and is less than half as likely to roll a 2.) Checking around online, it sounds like a homebrew falchion as a 2d4 weapon is a moderately common thing.