They should at least attack the blue/morale bar, so only low morale units are in danger/you can protect yourself by raising morale again.
Tbh, the fear attacks are not really a threat, but REALLY annoying to have 5+ pew sounds every turn from some psi attack. Dread is even worse.
Edit: I know that morale should have an influence, at least the tips tell you so. I didn't really see anything, everyone had 99/99+ morale and got controlled/feared like crazy.