I can understand their reluctance to sack Dyche.
As evidenced by lack of protests at the match etc, fans generally have understood it too. Particularly when most of us could appreciate no change was being made until ownership was resolved.
I'm sure loads will disagree, but their analytics/insights will be telling them this team is, realistically, placed in the league where it's expected to be. It's a team that averaged 41 points for 3 seasons before this one. We had a great run from April that pulled the average up but what's that saying around form being temporary? There's a reason the bookies only had 3 teams more tipped to go down before the season, and that factored in a Leicester deduction. Whether we like to admit it or not, we're crap. I personally think this squad is the worst we've had in the Premier League.
I can't see evidence of the team downing tools. They'll have sounded out sentiment towards the manager, and media friendly journos (not a fan of those antics from the club, and I'd hoped they'd stop until TFG...) have since parroted comments of players liking the manager. Any potential immediate uplift then from a new manager, is significantly lessened.
Their choice, whether Mancini, Mourinho, Allegri, Sarri, Southgate, Carsley, or whoever - is evidently only willing to come in the summer. Who can blame them? We're still the same team that Bielsa legged because it never had the players he felt to keep us up and left us with Dyche.
All that said, I think they're potentially going to misjudge the impact of having half a squad out of contract or loan, and an interim manager going into a relegation scrap. A team that can't score is always going to be bang in trouble - it's small margins down there, and a team with so many players and manager not invested in next season doesn't bode well. Ask Leicester with Madison, Tielemans.
Repeat the first 19 games again over the next, and odds are we go down. 7 times in the last 10 we'd have gone down with that points total.
All I could expect from Dyche was to keep us up, and then, keep our heads above water until there's new ownership and the ability to recruit. He did that. When TFG come in, we were above the drop and had a window to address recruitment failings. They've got to do that, and pronto.