In conclusion, while I 1) understand and can appreciate the goal of this proposal, and 2) think it would be
a way of addressing it, I don't think it would be the way I would recommend
for D&D. Predominantly because there are too many very-D&D things that would have to be completely re-worked to give it teeth (keeping magic weapons be a big score, figuring out how to make people pick up random weapons instead of pull out a backup same type of weapon, having people switch to monks and casters). Likewise, because I think other options (expanding 3e feat system or 5e24 weapon masteries to give positive incentives to switch weapons, adding back more creatures that take little-to-no damage from certain weapon types, other non-weapon ways of expanding fighter-action variety) would accomplish the same goal with fewer complications.
Instead, I think I would recommend this for another game, built from the ground up with these expectations in mind. It would:
- have fewer ways to carry 3 extra copies of your main weapon with you
- fewer ways to defeat monsters without a 'tough guy with weapons' out in front
- would not have finding very special magic weapons as loot be an iconic form of success in the game
- have much more consistency in what encounters you run into and how frequently those would be weapon-bearing humanoids
Perhaps most importantly, it would be a new system, one where there are no pre-conceived expectations, and you aren't taking anything away (from a game that previously doesn't exist) to achieve your goal. I would still look into whether an alternative method (varied attack-type actions) might achieve the larger goal of varied character action better than enforced variation of weapon type, if for no other reason than 'character with an iconic weapon' isn't specifically something I think shouldn't happen in a game or genre.