If you don't want druids to get +3 to the AC intended to their class, then why would you be opposed to a druid multiclassing or being the dwarf that gets medium armor as a race, or even as a feat? They are paying for the mechanical advantage. If it's balanced to go fighter then wizard (no armor normaly) and be in a full plate, i don't see why it's not balanced to go fighter then druid in full plate.
Totally aggree with you. Classes are mechanical tools and can often be refluffed. Barbarian that's a back alley brawler. Priest that's not a cleric but can officiate messes and weddings. Having your patron be a powerful dragon or playing a "warlock" that's a dragon sorcerer because you don't like the short rest mechanic.
Every member of a small native tribe can be barbarians, even the ones without class or the pacifist shaman.
You could be a member of the Druids without actually having the class. (range and nature cleric in particular, but even others).
You can be an assassin of any classes if it's your job.
Restriction on multiclass are so often stupidly justified. There's so many reason for pretty much any of them. Even the dreaded paly/warlock. I can understand the DM not letting someone be a oath of devotion/cleric of Lolth or an oath-breaker/cleric of pelor though.