Not really. Spells aren't that, and fighters (outside of 4e) haven't had much of that. Most classes throughout the editions were packages of stuff that everyone gets, combined with frequently duplicated abilities that everyone who's interested in gets. The truly class-exclusive abilities are exceptions and anachronisms, not what the game is "about".
And you can't built a new inclusive D&D by adding back in restrictions; that's for a DM to do.
They did, but they shouldn't have.
Again, that's the exception that makes people scratch their heads, not the principle on which the game was built. Early versions of the thief (and every other class) had all kinds of exclusive abilities and restrictions that have since been stripped away, most notably by folding thief skills into the skills that everyone gets starting with 3e.