I've thought that too. Having all primaries be elemental wouldn't make the game too easy, it would actually encourage players to strategize their loadouts even more for what element their primary has.
It could even be another thing to grind for, (like grinding for a god roll hawksaw, but also wanting a specific element).
I think it would be better to go with the Elemental Core idea. Having random elemental cores drop from high level content would get players to play that content (I used to grind VoG and CE for elemental primaries and raid exotics, but I've barely touched KF and WotM hard mode)
Plus, having the cores give a random element would create some more variety.