Hi - I'm not 100% certain that I understand this correctly, so please excuse any mistakes

Example:
I'm having initiative.
I play Exhaust on my opponent's Sage 2 to keep my Aspirants alive.
Sage 2 doesn't give a single f*ck and nukes away the poor little guys.
I think, that an exhausted Sage 2 should not be able to resolve his ability since the exhaustion-part is no longer possible. Of course the effect would apply to any creature with an ability payed with exhaustion, but the sages are the ones that probably hurt most.