Talksport did a poll not too long before he did end up getting the boot asking "would you have Ranieri at your club" and it was an overwhelming no.
While I don't give him no credit, I think he got very lucky as well. I don't buy this notion that he's transformed us into title winners overnight. He took over the form team of the country and had a world class midfielder signed (who he didn't even want, he had to be convinced daily). I think he made some tweaks during games, and I think he played a blinder with the media throughout the season as well (although I maintain this is the most overhyped part of football management) but you only have to see what he did when he actually had the time to have a pre-season to show that it's not entirely down to his methods that we won it.
As for Shakespeare, I'm not quite as confident as I was before, but at the same time I think recently his hands have been tied with squad selection. Our last three games we have been forced into playing a defence of Simpson, Benalouane, Fuchs and Chilwell. That's only one first choice player in their actual position. I cannot put the blame on Shakespeare too much when it's not his fault we lack depth, and he's been quite vocal about it too so I'm hopeful that he realises our issues.
I think it's imperative he stays at the club, but I wouldn't be disappointed if he went back to being an assistant to a new man.