I agree with your thoughts. Pochettino does have a lot of work to do but is currently on the right path with overhauling the squad - selling off players that have been ineffective to this Chelsea team in recent years. However, I feel Pochettino might do well in Chelsea despite what the odds are. I could remember when Klopp was made the new Liverpool head coach. The impacts didn't come immediately but eventually.
Chelsea management don't have enough patient. Pochettino's limiting factor might just be not having enough time to prove himself.
Actually, whether this is true or false, I think it still needs to be proven.
Indeed, streamlining the squad which last season had too many players is a very good thing, but in terms of performance I don't think it can be said to be true because it could also be a double-edged knife for them.
Pochettino can be said to be right in the overhaul when he managed to make some changes from Chelsea's performance and that can only be seen in the next season. but if in the end he fails, then the overhaul carried out by selling a lot of players this season can be said to be wrong in their initial steps.