Like I said earlier, the simple solution is to just nerf the shields or buff kinetic weapons. The best elemental weapons weren't used for their burn, like Fatebringer, VoC, or Mythoclast. Hell, the only elemental primary currently available, Zhalo, I forget that thing even has arc on it sometimes because it's just a plain good gun, I don't care about the element.
Endgame content should have something unique, and elements were that uniqueness.
On your edit, like I said, it made them unique, and it was still an added bonus to have the element, but not the biggest factor.
I've never tried to argue that elements were the primary reason that people used them, but it did affect other aspects of the game.
Whirlind's Curse is something unique on endgame primaries right now, as was Oracle Breaker, Wizard disorient, shooting through Knight shields, Cocoon, etc. Quillim's Terminus is still the best MG in the game to me because of Cocoon. All of those weapons do more damage against their own raid enemy types also. It's just more subtle than elements. I don't think we would have gotten Strikes readjusted to how they are today with elemental primaries still rampant.
I advocate for one of each type, but make them exotic. I'm not against the idea, just don't think there should be 20 of them running around.