You should know that Erik ten Hag was successful in his first season at Manchester United, because Erik ten Hag managed to make Manchester United finish in third place in his first season. Therefore, even if, for example, Erik ten Hag was at Chelsea and was successful like that in his first season, then of course Chelsea would not sack him either.
Chelsea is not like Manchester United, the owners don't give second chance and they're not relenting when the appointed coach in charge looks incompetent. Todd Boehly sack Mauricio Pochettino and was bad news for the Blues because Mauricio Pochettino have sealed the europa spot but couldn't convert his chances. Manchester United hooked up with Erik Ten Hag because he was the man for the job. He deliver quite exceptional tasks for the growth of the Red Devils. Erik Ten Hag would have been successful in Chelsea.
That is the problem we are having with Chelsea, the idea of always wanting their team to win trophies under the first season management of their new coaches which is never certain to happen. Chelsea started quite wrongly and of course took some time to adapt but later on they improved which they ended their Premier League season on the 6th position but looking back from where they came from, atleast Chelsea should have been considerate to retain Pochettino for a while because everyone believes his going to improve.
I think personally it would be the other way round, Pochettino will be more successful compared to Ten Hag if he managed United because they really fell out by ending below Chelsea.