In this situation we know that for this season and precisely at the end of the season Chelsea did not sack Poche but indeed Poche left on the basis of his own wishes where he preferred to resign rather than be at Chelsea next season.
Even if in the end Chelsea tried to keep Pochettino it would not be much different because Poche would still leave because there were several reasons that he must have including his relationship with Todd which was a little tenuous from mid-season.
This is a natural condition where surely he is not too willing with a big burden for Chelsea because seeing from the current situation for Chelsea coaches they are required to make performance improvements in their conditions which still need clear adaptation which will be very difficult to do even though the resources are abundant and any player they can buy but with less adaptation things like this are clearly a pressure on the coach's mentality.
Each club has its own way and policy in evaluating a coach performance, whether it is worth retaining or not. In this case, Pochettino was deemed to have failed to meet expectations so separation was inevitable. Arsenal did not act as aggressively as Chelsea, Arteta is still considered worthy of being kept, even though last season he failed to win a trophy, Arteta has shown signs of success. It is understandable that the two teams do not need to be compared, they will try to fight in their own way, and indeed Arsenal is currently better than Chelsea. Next season Enzo Maresca will be faced with a number of heavy burdens, bringing Chelsea to compete in the top four of the standings and finishing there when the season ends. To become a team challenging for the title, I think Chelsea still needs time, Arsenal and Manchester City still seem to be the most serious competitors.
As I said before it's not a sacking but a resignation and we can't say it's a sacking because I don't think it's objective and we can't blame Chelsea for not being with Pochettino because when Poche wants to resign why force it to stay in a relationship that's hard to explain because it's getting strained.
This is also not a matter of assessing failure or success because when this is said to be a failure for Poche then I think Chelsea management needs to review what failure and success are.
The first season managed to bring Chelsea to a slightly better position in a complicated situation that was very good for Poche, it's just that when he is not comfortable with the situation Chelsea has both in terms of performance and his relationship with Todd then forcing him to be at Chelsea will also only interfere with the professionalism that occurs so why force it.