There's definitely some big problems with the way saving throw proficiencies work right now, especially with multiclassing. The thing is, I don't think that allowing people to pick two saves is really going to fix the problems. For one thing, everyone will just pick Dex, Con or Wis, since those are the most valuable saves by far. Str, Int and Cha saves are rarely used, so are much less valuable. Of course, that is itself a problem that needs to be addressed. But even if they made all of the abilities equally useful for saves, you'd still have the problem where you only improve in two saves, while spellcasters get better at all of their spells - no matter which ability they target.
I think the best solution is either to give everyone prof. to all of their saves, or to just get rid of saving throw proficiencies altogether, and likewise remove the prof. bonus from spell save DCs. Those are really the only balanced solutions I've been able to think of.