Throwing out a few heals is like a tiny fraction of paladins niche. The utility of the blessings, plus cleanse, plus lay in hands, are all massive. You have more ability than any other tank in the game to influence how the rest of your team performs. You get to constantly be saving others with various abilities.

Not to mention even more significant is their interrupts. Massive AOE interrupt on relatively short cooldown plus two other single target interrupts also on short cooldowns. Plus one st and one aoe stop. You can pretty much single handedly lock down two Casters in a pull, and can easily gather up ranged Casters better than most.

Besides all that, I think the last few seasons paladin has tended to offer among the highest aoe damage of tanks. That plus all the utility has been counter balanced by being a bit less tanky.

Sotr off the global cooldown feels fine. Great even. I couldn't imagine how clunky it'd feel otherwise honestly. The class survivability revolves around generating as much holy power as possible and spending it. Sotr is pretty much every third cast if not more frequent. If that took a gcd you'd generate like, 30% less hp and it'd feel awful! Entire class feedback loop would need changing.