Coaches being there, while it may be one issue isn’t everything. However you’re also not paying attention, or just don’t care. Which is fine. But as you stated:
“ [If] the current coaches were giving them a reason to not sign, getting rid of those coaches might make them hold off from committing elsewhere.”
That first part of the sentence is 100% a fan/social media/ Cougarboard attitude. No teenager who’s never spent more than a weekend or a camp around the program is going to build a fan style narrative that specific coaches need to be fired before they’d consider going to school there.
Anyway, you’re technically correct. It is possible.