Do you think a big time coach would come here?
In every practical respect, this question is irrelevant. Stoops is the winningest coach in UK football history, and is signed to a long term contract. He is a far better coach than this thread suggests. People don't appreciate what they have until they lose it. Stoops recruits far better classes than previous UK coaches could. Stoops has the backing of the Board and President Capiluoto. He doesn't want to leave, and he isn't going anywhere.
To answer the question, though, there is no standardized definition for "big time coach" and opinions vary. If our HC position was open, which it won't be anytime soon, people would be surprised at the quality of the candidate list. All of UK's football facilities have been modernized, Our conditioning facilities are very high level. The roster is good enough that a smart new coach could come in and win immediately as long as he connected with the returning Wildcats. The snafu has always been that UK's core recruiting territory is problematic and limited. But our recruiting budget has increased steadily, and Stoops has proven UK can attract good players out of adjacent states as well as MI, PA, FL, and GA.
Of course, the negative posters insist UK could not attract a "big name coach" in the context of this thread. But many negative posters, probably including some of these same people on this thread, have campaigned in the past for UK to hire Steve Spurrier, Bobby Petrino, and Jim Tressel. So it is a hypothetical question that hasn't been tested since 2012, and the situation has changed since then.