Pochettino's burden is very heavy because Chelsea is currently a team that is in a very downturn and right now they are overhauling a lot of players in the squad so Pochettino has to reorganize this team from the start.
If you want to make Chelsea a top team again, Pochettino needs a process and time. I have a little doubt on the part of Chelsea's management, whether they will be patient because last season, as we know, Chelsea's management made decisions very recklessly which harmed this team.
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.