Chelsea's problem is not what any coach can solve in a short time. Since Chelsea is in the stage of rebuilding its team, they need to give their coach time to understand his players and know the best tactics to use to perform well and take Chelsea back to their glory days. Pochettino's performance at the beginning of this season was bad, but when the season was coming to an end, Pochettino started winning matches in the Premier League and finished in the 6th position in the Premier League table. Todd Boehly would have allowed Pochettino to remain Chelsea's coach because Pochettino could have performed better in the new Premier League season.
Everyone will look back at how Pochettino will handle the Chelsea team next season after Chelsea's poor performance last season, because I also believe that Pochettino already has several tactics that are suitable for him to apply again to Chelsea next season by trying his best from the start of next season. The Chelsea team is indeed in trouble, but this is also not the only obstacle for Chelsea to recover with better goals for a full season with the same coach, namely Pochettino.