No manager would want to take up a managerial job in a top club like Chelsea and get sacked before six months of his reign at the club and that I think is Chelsea's main problem in getting a another good manager at the moment.
The now club owner was busy buying good quality players instead of buying players that were needed for the club. The mouth watering amount of money used in getting the services of Enzo Fernandez would've been used to solve the current attacking issues at the club. Chelsea I think needs a very sharp no. 9 striker to compliment the great midfield line they have already and without that, any manager that comes to to club will still flop
That's why as reported by some sports media. that Nagelmann and Luis Enrique, have several requirements that must be met by Chelsea if they want to use their services. from Nagelsmann's side, it looks like he has learned a lot with what happened to him after his dismissal by Bayern Munich's management.
Luis Enrique, he also has a number of requirements that were submitted to Chelsea if he wanted to use his services as a coach. but it seems now the rumors are blowing stronger towards Pochettino. I don't know why Chelsea made it a top priority, or whether it was difficult for them to bring in a coach with more experience and potential. so I see, this problem is in the management of Chelsea itself.
Well, as you also said, I agree, that Chelsea needs player number 9 who is sharp in terms of scoring goals. because, the players currently available are unable to prove their ability to score goals. it's just that, the first problem lies with the coach and roughly, which coach is capable of bringing Chelsea in a better direction.