An "acceptable" theory of everything is quite a matter of taste.
Since all your experiences are grounded in classical physics, you feel that quantum mechanics is unnatural and seek to "understand" it, probably in terms of your classical notions. For eg: Do you ever question Newton's first law... why should objects have a property called inertia?
Some people have accepted quantum mechanics as the fundamental framework and that our naive classical notions are simply an approximation to quantum mechanics in some regime (day-to-day life). If that was your perspective, then there would be no need for a theory of everything to "explain" quantum mechanics. QM would be an obvious input and the theory would have to predict/explain everything else that you observe.
Roughly speaking, any physical theory has to have something you put in (axioms) and some thing you get out (theorems). At the moment, to me, it seems unlikely that we might be able to find a theory which is unique, compelling, and self-evident, without needing any axioms. It would be wonderful if such a theory existed and if we found it, but I think we're going to take a long while before we get a handle on the question of whether that's possible. But hey, that's just my opinion. The concept is definitely fun to ponder about ;-)