Cover should be a Role Action

[ItMe]

That would likely just lead to them doing what they do with interrupts: Once per tier there is a ability (usually cast by a add) that requires an interrupt to avoid a wipe.

This is true, but they could always change what it does.
As an off the wall example: what if instead of reducing damage to people behind you it blocked off orange AoE markers? Something as simple as that would definitely influence strats.