I'm not saying it isn't possible for a coach to come here and immediately improve the team, but the likelihood of that is probably in the single digits. Honestly, out of the 4 you mentioned, only Brohm and Cutcliffe did anything extraordinary in their first three years, WSU and Kansas had higher floors when their respective coaches took over than many remember, and MacIntyre had a pretty pedestrian start. Illinois football has been the worst P5 team in the past 15 years, our point right now is in the bottom forth of those 15 years also. Firing Lovie will make this team worse for the next three years barring a proven coach who can bring in instant impact freshman and actually coach (hint there is no one out there that can claim this with certainty and is available for UI).If the baseline of the previous coach is F/+ ratings in the -30% range, there's no reason to think that's the case. The Purdue case is a rare one where the change was huge and overnight, but coaches who are going to improve wasteland jobs show much more competitiveness immediately. Mike MacIntyre at Colorado, David Cutcliffe at Duke, Mike Leach at Washington State and Mark Mangino at Kansas would be some examples. None of them set the world on fire early, neither on the field nor in recruiting, but they all markedly improved what they inherited right away.
Also, roster turnover during a coaching change is usually less than you'd think. If we fired Lovie right now that would probably cost us IW and Beason, which would be bad and is one reason it's a bad idea, but mass exodus of players is pretty rare. Players on low-talent losing teams don't have a ton of other great options.
It's kinda two sides of the same coin, a coaching change shouldn't be irrationally feared, nor should a new coach being a total disaster early be written off as the cost of doing business. I remain hopeful about Lovie, but if it doesn't work out, it was a very significant clue that he inherited a team that was +0.2% in 2015 and had the floor fall out on him in year 1 to -25.3% with a fairly veteran team operating with a full compliment of scholarship players.
Also, I never said there will be a mass exodus, but you point to exactly what I meant. Top talent will have the oppertunity to leave. On most teams, it doesn't matter a whole lot, but we have very few guys who we rely on heavily. If they leave, this program tumbles further (and yes, there is room to become worse, even in advanced metrics, let alone eye tests).
There will be a point (sooner rather than later) that we find out whether Lovie can coach a top half B1G program consistently, but it isn't until after next season at the earliest. I will say Lovie should've done better since he took over, and his refusal to play anyone but his own recruits almost certainly cost him wins (or at the very least point differential). Sure Beckman/Cubit left the cupboard about as bare as it gets, but there should've been better (not by much) outcomes earlier. He will ultimately be judged on his players though.