Mauricio Pochettino is an experienced coach in the Premier League and to improve the performance of a team that has fallen down like Chelsea is not an easy thing especially with high targets, everything needs process and time.
Chelsea's management must learn from their mistakes this season, as a result of their reckless mistake in making the decision to fire coach Tauchel and buy several players at high prices, but not everything went as expected.
Since Chelsea's management changed, they have done many detrimental things as if they didn't understand, so this team is getting worse.
There is no other word for building this team other than process and time, like several other top teams that have also slumped, they all took a while to get back up.
Mismanagement is one of the reasons why Chelsea have suffered such a drastic drop in form, but I don't think it's the only reason. However, this is a normal situation in the midst of a club in transition from old management to new management. Chelsea added too many new players in one season and this is also a big problem. Instead of expecting them to play well but in reality they fail to connect well with their teammates. The players need a period of adaptation, but the coach is also considered to have failed in managing it.
Tuchel also could never guarantee Chelsea's performance would be good compared to the other two coaches if Chelsea didn't fire him. He also had a lot of obstacles in his last tenure at Chelsea, so Chelsea weren't 100% wrong about that decision even though some thought it was too soon. So now Pochettino is expected to turn a new leaf for Chelsea because of his experience, but he has a tough job and it's going to be a lot of pressure.