I feel there are many ways to skin this. There is no one right way.
@EzekielRaiden's idea seems to address the multiclassing issue quite well, far better than the feat option we have now.
@Maxperson is right in that we'd lose a vital section of the game for some of us.
But ultimately what is the concern is the power curve, that feels off. Similar to some other current threads at the moment at least two that I can think of, both of which deal with magic and their comparison to martial.
What D&D suffers from is not having enough in-built levers (from my view point). Too many of us, too many playstyles to cater for.
Cantrip options. Hit Point bloat. Spell cost. Maintaining Bounded Accuracy in a system with Expertise and Magic Item plusses.
In the end, D&D has always been one for the Tinkerers.
I'm curious if the guys that play the independent games tinker with the rules with their games as much as the D&Ders. I seriously doubt they do.