If you remove healing thing from tanks then nobody will solo maps anymore. Most people enjoy soloing maps and so do I. I have done plenty of new level 100 map solo on either Paladin or Warrior. It's not easy but with proper cooldown management it's possible. May also had better experience with Paladin as I endured more than with Warrior.

GNB and DRK are the ones that can't solo anything reliably as they have meager heals and that's totally fine. Not every tank should be equal.

Edit: Heals from warr are also useful when you run dungeons with people who are afk, stand in aoes, die 99x times and say "sorry first time" and chat more than they follow mechanics, yeah. Your abilities may save someone and prolong dungeon run instead of wipe.