Brief Thoughts on Damage Types

Gotta get these thoughts out of my head so I can focus on other projects at hand.

These days, I don't even play D&D 5e, but I chat with people who are influenced by it now and then. The other time, we had a talk about the damage types, and I figured I'll try to express myself in regards to those. I don't like how 5e does the non-casters dirty. Sure you get to pick a weapon, but largely it doesn't matter because most creatures who are resistant or immune to one are resistant or immune to all three of the weapon damage types: bludgeoning, piercing, slashing. How could this be remedied?

1. Non-BPS Weapons. Give non-casters decent weapons that don't deal bludgeoning, piercing, or slashing damage. Torch as a weapon is a joke, 1 fire damage might be good for burning a rope or whatnot, but not in an actual battle. Yes, you could get some kind of magical flame sword, but magic items are given out at DM's discretion, and spells are the domain of spellcasters. Non-casters need weapons that they can choose which don't deal BPS damage.
2. Two out of Three. A monster is at most resistant or immune to two out of Bludgeoning, Piercing, and Slashing damage, or at least the vast majority are. If they are as common as they are in 5e, the DM is actually obliged to give the non-casters magic weapons. They might be happy about it, but those completely step over the problem and lead right back into "BPS doesn't matter" category. Player characters would thus have to carry multiple weapons on their body.
1. Tangent: When I discussed this online, people brought up that most players picture wielding a single weapon, to which I say "Yes, but even that weapon can be situationally swapped out". How do you expect a greataxe-wielding barbarian to fight flying foes? Yes, with those javelins that they in their equipment by default. Characters in fiction swap their weapons when necessary. There's also the fact that you can't play a pure pyromancer or cryomancer in this game, it's pretty much the same problem: the game expects the casters to pick multiple spells with different damage types, and it doesn't offer enough spells for most damage types anyway to fill out your spell list. Even sticking to a single damage type you could be picking up buff, debuff, and utility spells. A player's "aesthetic" for a character can expand. And by having to carry multiple weapons on their body, suddenly magic weapons don't get devalued as fast, just because "this +1 dagger is worse than that +2 dagger of Teleport behind the Enemy".
2. Also, I know that there would be problems like balancing out how many magic weapons does which player get and such, I will admit I haven't given it too much thought since I'm trying to focus on my other projects these days. These are just raw, unprocessed ideas.
3. Also-also, maybe this wouldn't be necessary if non-casters indeed got good Non-BPS Weapons, see point 1.
3. Monstrous Traits. Monsters could have traits that trigger upon taking specific damage types. Not just BPS, but still broadly applicable and I think it'd enhance the game.

• When (insert some ooze here) takes slashing damage that's less than 5, it splits into two, each with half of the original's remaining HP. (Note: Maybe one of the oozes in 2014 Monster Manual does this, I honestly can't tell because it's been forever since the last time I've opened it).
• When a mind flayer would take psychic damage (but doesn't because it's immune), it can locate the source.
• When a shadow takes radiant damage, it can't hide during its next turn, or it has a disadvantage on all of its rolls as per the Sunlight Weakness.

That's about it for now. Some simple ideas.