I don't like Pochettino's coaching style. He likes buying already-established players. I will not be wrong if I assume that he depends on big names to win trophies. I am more comfortable with coaches that build young players. Coaches that groom unknown players to superstars are the best in the world.
Pochettino is a great coach who loves to play pure attacking football, he of course didn't win any trophies in Tottenham, neither did the club have the money to buy "already eatablished players" like you say, Pochettino did so well to play good football with the players at his disposal when he was in Spurs.
Having said that, Poch won trophies in PSG and that's all the trophies that he has won, mind you that most of the transfers that take place in PSG is done solely by the club, without even the managers consent, and that's the same thing happening in Chelsea now, Todd Boehly is just buying players left, right and center, none of them have been players that the manager identified himself. Chelsea are doing crazy business right now, hiring too many players, many of which they don't even need.
Yes, that's right, Pochettino is a typical coach who plays attacking football, even though he once won the title with Tottenham, he is able to manage a team filled with mediocre level players and become a force that is quite feared by opponents.
Currently Pochettino is in a transition period at Chelsea and of course he needs time. He has also inherited a number of talented young players who were brought in by management without his interference. In my opinion, the job that Pochettino took was quite challenging because none of the players he recommended in the current Blues squad. But if Chelsea management can be patient, maybe Pochettino will be able to form a great squad next season. I also believe that the Argentine man will bring about rapid changes, even if not in the near future.