In my view, Chelsea is not a team that has patience and Chelsea is a team that cannot respect the process. Because anyway, if Chelsea can respect the process and give a second chance, then surely Pochettino can still do his best for his second season later. Indeed, Pochettino failed but anyway, in the end Pochettino also managed to make better results for Chelsea. So yes, even though Chelsea will appoint a new coach for next season but anyway, if for example the new coach cannot provide good results for Chelsea later in his first season. Then of course, Chelsea will do the same thing will sack the coach, because sacking the coach at Chelsea seems to have become their standard when the team fails to finish in the top four.
We are too quick to judge Chelsea on how they change their manager frequently when they are not delivering their work effectively as the management desire without realizing that they are running a business which requires a positive result in order to progress. Chelsea as a club is like a company and no company will continue to hire you and keep on paying you if you are not making impact on the progress of the company. I understand the importance of patience with couches in order to allow them to build a formidable team in the long run but if it takes forever to build the team, it means the couch has no idea or strategies to make it a reality. Besides, there are signs to see in a team and one would be able to tell whether the couch deserves more time to prove himself.
We shouldn't attribute this attitude to Chelsea alone because every club will do same when they are not getting desired result from the couch they appoint. You as individual can not keep a property that has no benefit or value to you for longer period talk more of a group of people who aim big as a club to be recognized as one of the best in all competitions.