Yet I cannot bring myself to switch to a magic user. Oddly enough, I didn't have this trouble in Morrowind or Oblivion yet here I am, having trouble making one in Skyrim.

Stealth classes are fine, though.

I think the problme here is that you aren't killing fast enough. If not, then can you explain what it is.

When you get destruction up to level 40, you can get a perk called impact which makes you unstoppable.

Maybe bridge the gap. Try a battlemage instead of a full blown magic user.

^^ This. Then slowly ween yourself off of weapons.

Uh, no. I just can't get into a magic user for some reason, or at least a pure one since spellswords and battlemages are pretty fun. I just find the idea of only using spells boring.

Agreed.

PURE mages aren't necessarily powerful as in the previous games.