Chelsea should be able to put trust in every coach they employ, like Ten Hag at Manchester United and Arsenal with Artata. Not all coaches are able to do a great job in just one first season, even if it is not impossible, it will be really difficult because of the adaptation process.
Chelsea is completely different from other elite EPL club. They're strict when it comes to their managers and not welcoming any relenting outcomes. Erik Ten Hag in Chelsea? He would have been sacked long time ago. The previous owner, Abramovic doesn't welcome any relenting efforts or if he sensed any form of incompetence from the headcoach, he will definitely make good use of the sack letter.
It's not about having trust in their couch, it's their tradition and I don't blame them because I will definitely do the same thing if I should be in their shoes. Take a look at Ten Hang in Manchester united since you used him as example, can you continue to have trust in such couch if you are the owner of the club? I guess your answer will be No. I know it takes more than just a season to build a team but even at the beginning, there suppose to be signs to show that the team is on the right track and the couch is worthy to be given more years to build a dream team but what can you tell of Ten Hang at Manchester united to prove he should be trusted for more seasons?
If Ten Hang is in Chelsea, he would have been the least serving couch in the club if his performance will be as same as it is now in Manchester united. I like how Abrahamovic was making good use of his sack letter because some of these couches are just there to earn a living without impact on the club development. Todd is too calm and tolerate what shouldn't be tolerated in order to maintain the standard of the club.