There's a difference between being good at something and being non-functional.

The difference between White mage's aoe healing kit and what Scholar and Astrologian have is one of basic functionality. Remove Indomitable and Earthly Star and they're going to have a significantly more difficult time dealing with AoE damage. Not a little more, but to the point where they'd not be functional. having what you need to deal with a scenario, and having it in ample quantities is the difference.

Shields are just one part of mitigation, and there's a fair amount of it across the non-healers that even in double Wham scenarios, you can survive without shields, and have more than enough healing power to get people back up. The job isn't non-functional for lacking the tool. Get rid of Indomintable and Earthly Star and I doubt you can say the same for Scholar and Ast, let alone double Sch / Double ast.