Hybrid classes - SAM & RD MAGE.

[Reynhart]

I really don't see why it should be so difficult to balance though, or why one would think that the game forbids a job from being good at two roles at once.

The problem here is balance. If one job can be good at two things at once, why bother bringing another job ?
By preventing changing "on the fly", it can reduce the problem, just like AST won't be able to switch stance during combat.

As for BRD, they trade mobility for damage, and, having recently done Keeper Of The Lake as a BLM instead of a DRG, mobility can be a very important loss.
They purposely didn't make BRD a top DPS and an important buffer while keeping mobility.