I actually don't know if that's really a huge concern - if the WHO burned their public trust they could always be publicly dismantled and replaced with a new committee[1] - these outbreaks happen rarely enough that public memory isn't going to sustain that well across multiple failures.

Good behavior induced by fear is a real asset in pandemics so we need to not be hesitant to use it.

1. A.k.a. "The Blackwater Approach"