You can fix this by starting at a higher level, by not allowing multiclassing, or by having a completely separate class writeup for people who multiclass in.
Actually, given how the playtest has been shaking up so far, I think they could go pretty far with making feats and specialties more expansive, and doing away with "multi-classing" as we know it.

You class defines your core, it is who you are at the most basic level. Then have feats encompass minor versions of class features and be available to all (much the way "Arcane Dabbler" does now). Are you a fighter that does some magic, great, take Arcane Dabbler and maybe later on (at higher levels) some feats might grant you some regular level spells too, but you will never be as good as the wizard at spells. Similarly, want to be a wizard that mixes it up from time to time, take some feats that maybe give you access to some better HP, AC or to-hits, and maybe at higher levels, limited CS dice, but you will never be as good as a real fighter. Eliminates the problems with front loading without having to deal with starting at a higher level (and all that entails) and gets rid of nasty experience progression issues too.

From my POV, part of what makes D&D attractive to me personally is the baseline flavor, such as the cosmology of Inner and Outer Planes, the grumpy Dwarf, the haughty Elf, etc. It helps me have a common expected starting point from which to build upon.

Perhaps that is me and me alone... I am guessing that there are many others who feel the same way to more or less degrees, but of course that is just my guess.
I agree, I'm happy with light flavor in D&D. If I want to play GURPS, I'll play GURPS, but I want D&D, which includes some basic shared tropes.