There’s no way at the start of the season we’d have envisaged Koeman not being here (good or bad) 9 PL games into the season.
That said; once the crowd’s mood had turned to such a degree (after the Burnley game) then they should have really ramped up the list of potential options.
That list should have been based on medium to long term, well as relative as that can be with managers, options as you don’t / shouldn’t sack someone whose PL record was 7th, 6th, 7th in the first third of a season unless you think that they’re massively under performing with the players at their disposal.
We clearly didn’t do that as the options list, at least the reported one, had no cohesion of approach.
However whatever the wrongs of all that we should still be careful with this appointment unless we’re making a sensible “end of season” appointment to buy us time.