There wouldn't be a media backlash. For one thing, the media only learns of a coach getting sacked after the fact--so any backlash would be pointless.
For me, being an //above average// team that can get into the tournament every year but can't get beyond the Sweet 16 or become a genuine contender would be the //worst-case// scenario. Then you are just muddling along year after year after year--which is essentially what we've been doing for the last 15 years. I'd much rather we be terrible for a couple of years, lose the coach and make a real effort to find a genuinely talented coach/proven winner. There's always a risk in sacking a coach who's been doing just enough to stick, but it would be a risk I'd be wiling to take.
That's what happened years ago on the men's side with Coach Don Devoe. He was a solid coach, but not very dynamic personally and not a very good recruiter, and thus the Vols with him were respectable, above average--but not good. And he was sacked, and I believe his successors had even less success than he did. So there's the risk of going from mediocre/above average to poor, to be sure--but programs with our pedigree should be willing to take that risk, IMO. I want Harper to succeed, but she's not shown me a lot thus far. She's a better coach than Warlick, but a worse recruiter and we're still basically muddling along--and we muddled along this year despite having two of the top 20 players in America, I believe.