Oh definitely. We hired a fig leaf guy to give cover to the Admin for the search. That was the Golden search, iirc.
There's not that big a universe of coaches. Search firms are useful for reasons which don't really apply to coaching vacancies. They can give you reach to find and screen interested people you don't know about -- this can be hard both because the business world is big, and because people with jobs are naturally cautious about taking calls from someone who isn't their employer. Search firms are good at pretending they're asking for 'advice' or a reference on someone. They can help you create awareness of the opening, also, amongst potentially interested parties. They can run quiet searches if circumstances warrant that. Yes they can help you assess people and think through the spec. But it's more about reach and filtering. In football, the universe of candidates isn't huge and the job opportunity isn't a secret. Every potentially credible candidate already knows Miami's headed for a search and knows how to reach out. Also, coaches have agents to reach out through, which already makes them different from managers who search firms tend to reach out to.
Nothing against a search firm at all, they serve purposes and there's a role for them. But UM doesn't need more outside advice so much as it needs first to step up and own its own situation. No search will work if the people leading the search are clueless, unfocused, don't care, don't know what they need, etc.