#1 It would affect their stability
Regardless of who arrives as Chelsea's new manager, the club's stability is bound to be affected.
It is a well-known fact that every new manager comes with new coaching methods, tactical variants, training regimes, and sometimes dietary regulations and the players would find themselves in a situation where they have to start adapting to the new manager's methods.
Indeed, they had only just gotten used to Sarri's style which ran in stark contrast to his predecessor Conte's, and this is a far from ideal situation for the club's players to be in.
This goes in contrast with Chelsea's major rivals in the Premier League - Pep Guardiola has been at the helm at City for the last three years and has molded the Cityzens into an unstoppable winning machine, Liverpool are the strongest they have been in decades thanks to Jurgen Kloop, and Tottenham have maintained consistency under Pochetino for the last five years.
The appointment of a new manager means that the players might take some time to adapt to his methods, and when they eventually do, they might find themselves with a higher mountain to climb in their quest to rise to the summit of English football once again.