First of all pretty much every club that replaced a manager this season went backwards or at least didn't improve any - Aberdeen, Hibs, Dundee, St. Mirren. You could even argue Rangers went backwards, at least in terms of their league challenge when Gerard left.
The idea that you replace the manager and things get better just doesn't stand up. The context of the Scottish league is such that the major problems for any manager don't actually change any by replacing one for another, especially when the main thread of criticism is 'better style of football'. The players just aren't there to play good football. Across the league we export anyone with a hint of talent almost immediately. Season after season after season of sold off talent is why we are where we are. At Motherwell and pretty much across Scotland. Only Rangers and Celtic have the millions to replace who they sell.
Secondly if you look at the clubs that actually got top 6, they were all managers that were supported by their clubs through quite severe criticism from fans that, quite frankly, often are more concerned about cathartic output than level headed analysis.
Hearts fans were desperate for Robbie Neilson to start badly this term so they could continue their Jettison The Manager campaign. Ross County waited till round 11 of the season before they got a win, Dundee Utd had the second worst run of defeats (6) and had a run of 2 wins in 16 mid season. Yet by sticking by the manager they all achieved top 6 finishes.
Meanwhile, outside the Top 6, Hibs and their clown owner fired two managers and are currently 8th in the league on a run of 2 wins in 16. The same record Aberdeen currently have although they are even more lowly in 10th. Dundee sacked a manager and haven't won a game since, while St Johnstone stuck with Davidson, despite 8 losses in a row (the worst run of any team this season) and they might well survive. Certainly they have a better chance.
I've been arguing for year and years about the steep decline of Scottish football. When we do relatively well people don't want to hear because they feel it is a sort of attack on the achievements of the team. When we do poorly folk make the usual reflex kick at the managers and pile 25 years of game wide mismanagement across Scottish football on a provincial coach a season and a half in.
It's time supporters start actually talking a wider view on the poor standards of Scottish football. Every single manager in this league, newly appointed or not, is swimming against a tide of decline decades old.