I would like to submit that the Paladin's "Primary Gameplay Mechanic" is their unique possession(among the tanks, at least) of both Reactive Utility and Utility that specifically targets party members instead of enemies. Basically, their shtick is that they're the best at actively protecting the Party and getting it back on its feet when things are starting to go sour. This, of course, ignores the perceived effectiveness of this Utility, which you have covered further down in your post. Regardless, when we ask "what does a Paladin manage that the other Tanks don't?", their spread of party based utility rings the bell.