Fanaelialae
Legend
3e multi-classing has only two problems: (1) cherrypicking the first level of a frontloaded class
There are a few ways to address this issue. The direction I'd currently lean would be to frontload all classes with a starting level package of abilities (for a fighter weapon profs, armor profs, fighter's mark/challenge, opportunity attacks, etc.). However, spread those same abilities throughout the progression. (If you gained it at level 1, you don't also gain it again in the progression, because it's just there for multi-classing.)
Someone multi-classing in to a new class doesn't get the starter package (they just get the non-packaged 1st level abilities). If they stick with the new class, they can eventually earn most or all of the starter abilities, as well as advanced abilities.
I think this reflects the idea of multi-classing better. It always rubbed me the wrong way that a fighter can multi-class into wizard and suddenly gain what supposedly took the wizard a decade of apprenticeship to learn. This way he might be stuck with cantrips during his 1st level of wizard (because in this hypothetical, 1st level spells are part of the starter package). Eventually though, if he sticks to his arcane studies, he might be almost as good as his friend who started as a wizard. Plus, he has some nice fighter tricks to fall back upon if need be.
As to your 2nd point about multi-classing, I couldn't agree more.
And fwiw, I've got nothing against grognards.