Dont think Tata would have lasted another season and yes do think Barca would sack a manager on back of season Ancelotti had.
Lucho would have been gone had he won nothing. Would possibly not even have lasted the season if things didnt turn around.
While you are making very valid points I think you are ignoring some political aspects
1-Barca or RM,at the end of the days those clubs are controlled by individuals and no matter how much ppl try to deny it,the change of individual changes the way decisions is made. Different boards made different decision,I think Laporta sticking to Rijkaard with Crujif advice as something that non of RM board would have done tbh
2-Managers are usually the hardest piece of the puzzle for boards. It is easier to make fans excited about signing player X or Y than about having a new coach,it is harder to get a coach and work with him on his philosophy,at the end the board is mostly men in suits not football people.
-In Barca the different boards we had preferred stability,they simply hated change specially the Rossel/Borto boards,when we had to change Pep we went for his predecessor,then we had Tata after health issues specially with no clear replacement from inside,after that we brought our former Barca B coach back.
Why?They want the easiest way,that is why Lucho had a contract renewal past summer and probably he would have stayed next season if he wanted.
That said they won't risk themselves for the coach,when it is politically their best interest to fire coach to protect themselves or win the fans back they will do it.
-In RM? They have it differently, They had two presidents in this millennium,Perez and Calderon
Perez stayed all but 3 years,the guy reached a point that there is almost zero threat to his place. And yet he changes managers easier
Benitez was fired too soon even if it has proven to be right decision,RM fans wanted Ancelotti to stay and he was fired after 2 years,only 1 manager stayed for 3 seasons since Del Bosque
I think we have to fair with our boards and give them credits for that matter tbh.
Dont think there is that image or any great difference in how top european teams are seen as being cut throat to managers that fail.
I think you are wrong in terms of people perception,people see how RM fired a coach the fans wanted to stay in Ancelotti,they remember how Calderon sacked Capello too.While they see that since 2008 Barca had 4 coaches and only 1 was fired,they see remember Barca sticking to Rijkaard after 1st bad half season,sticking to Lucho after 1st half bad season,sticking to Tito after 0-7 SF defeat in CL,3 managers staying 5,4,3 years in the past 14 years and one of the other two could have stayed longer if it wasn't for his illness. I think the public perception in that regard is very clear