The game already works like this. Automatons and terminids behave extremely differently, and push for very different weapons. And in each faction some enemies will be more easily dealt with with specific weapons.
Two infamous examples are the berzerker bot and the stalker bug. Control weapons (weapons with high stagger) trivialise them. But most people don’t use these weapons, and thus those enemies are among the most hated ones by the community.
People mistaken fun and trivializing.
The game is balanced around being difficult, so that you need your team and stratagems (weapons included) to beat it.
When you get a new overpowered weapon, it feels great because the game is so hard/tedious otherwise. But it is actually an overpowered weapon.