You're assuming any of those men would have wanted the job. I'm not even sure Carsley did TBH.
I don't disagree that some of his squad picks have been iffy, but few England managers ever please everyone. I think a decent side will make mincemeat of our defence, but plenty of teams grow as tournaments progress, we've topped the group, unbeaten and scored 6 goals and that's kinda base requirements for the group stage. Gets harder from here on in and you can only rely on Bellingham and Kane so much.
I think if we don't at least make the quarter finals he's gone.