Already it has been analyzed that Manchester United's problem now is a coach so they should fire Ten Haag and bring in another coach to continue the managerial duty and that is actually what Manchester united needs for now. I can't totally say that Eric Ten Haag is not doing his best for the team but he needs to leave the club now because he has tried but his techniques is not working for the team are all.
Whatever Man United decision to fire Erik Ten Hag will still have consequences which the new coach in his first season may not be able to match. According to many rumors, Ten Hag will stay for the next season, which is quite annoying news for some United fans but others are trying to give him a chance. For me Erik Ten Hag needs to lower his ego a lot, where so far he always wants to feel right about himself and rarely listens to input from other people and also input from his own players. As a result on the field the players were not seen playing freely, stuck to monotonous strategies and it was all Erik Ten Hag fault. So before blaming the players the quality of the coach must first be questioned.
Next season other teams will start to develop, including Chelsea, which is slowly showing positive results. If Man United continues not to change its game, it is possible that it will fall further behind. If we finish above 7th this season, it will be a bad record and Erik Ten Hag will definitely be blamed.
Literally before Manchester United can come back to good form now it will absolutely take a lot of time no matter the coach they would want to hire now so that is it because to build Manchester United now is a very big task for any coach at all because the first work will be to build the mindset of the players to be able to align with the coach, having a good relationship and understanding between the Coach and the players is very important. Manchester United allowing Eric Ten Haag to still continue next season might cost the club chaos because I don't see him making any difference next season but retaining him could be if he makes some improvements for the club if not I see no reason retaining him when he is not doing well.
About Chelsea improving from next season is not certain because they are literally facing same problems of coach with Manchester united so until they sign a coach that can rebuild the team again, they might even get worst next season. I assume you want to say that if Manchester city finish below 7th position instead of below 7th position but however, regardless of their current drop in performance, they can still finish within the 6th or 7th position before the league ends.