Pochettino knows that he is going to be forced to just develop the team gradually, one by one, step by step. But the owner is spending so much money on the team so he wants some results right away. In football world you do not get results right away, that is just not how it works at all, you do not end up with good players and good situations all the time, you just end up with getting better with time.
But, the owner is some rich American, of course he doesn't understand how it works. In their world, they could spend money to some sign stars at Free Agency and then be a good team, so he looks at how much players at America makes, and how much they are spending on transfers here, and he thinks that they should have some awesome team.
In football that is not how it works at all, that is why I prefer INEOS approach, they are spending more clearly and cleverly now, and that means that we are going to see United do much better than Chelsea. Both were taken over by their owners around the same time give or take, but United has done better because they know it will take some time, so they focus on great young players that have good potential to help them on the long run to gradually become better.
Sacking pochettino was not due to the performance of the season but had to do with the transfer arrangement, pochettino want to be in charge of the players to be signed but Todd borely does not agree with that because he is a business man and he wants to maximize profit, so Todd borely tactics in the transfer market is to sign young talented players and give them a very long term contract, and send out some on loan and sell them for a higher price than he purchased them, why pochettino want some experienced players in his team so they can challenge for titles.
So this is what trigger the sack of maricio pochettino, if not the management where convinced with his performance and wanted to give his project time, but due to the reasons above both of parties have to path ways.
So far, I will say Enzo maresca will do a good job in Chelsea if he is given time. They have a lot of quality players already and they are also signing more quality players, with the right philosophy I think Enzo maresca project is one to watch out for in the premier league next season.