Point was: they’re that wound up about something as “don’t worry about it” as used-once batteries (for “can’t be wired” situations). If they’re that uptight, they should be ensuring “too close to the mic” isn’t a problem.
If a performer notices a preventable sound system problem - especially if it’s bad enough the performer breaks form/show and complains about it on stage - the sound tech failed and won’t be trusted anymore.
In the concert situations I have experience with that kind of mistake puts your job seriously at risk, or gets your entire company fired from the tour.