This is mostly because AST has two sects: Nocturnal and Diurnal.

If you get two ASTs in the group there is no reason for both to be Diurnal or both Nocturnal. They should always be opposite sects (one Noct and one Diur) to work together with highest efficiency since Noct and Diur stuff does stack with each other.

When you get two WHMs in the group they have no stances to change to so to penalize them just because they happen to DF and get two wouldn't be a good thing to do.
Why not? Two SCHs already get penalized with non-stacking barriers.

I really enjoy this job, but the cards feel like a gimmick instead of a focus.
That's exactly what was intended. The job is still a healer, first and foremost.

It's the exact same deal with BRD and its songs. It is nowhere near the support level it was in a game like FFXI because here it is still a DPS, first and foremost.