Regardless of the nonsense people believe about money spending, high money spend should get you in the ballpark to compete every year, doesn't mean you will win every year nor that you are favourites. Most teams with a new manager will be better in the second year(a good manager that is) than the first. Teams take time to adjust, no matter how competitive they were or weren't the year before.
I fully expected City and Chelsea to improve with better managers, and they have. Neither team is in precisely the same situation, City have had more problems with Kompany and Aguero this year. Chelsea have been much better overall, and a lot of their bigger spending has been on younger players like Hazard/Oscar, rather than buying 24-30 year old players which in general gets your a more finished product and often players who will settle more quickly simply by being more mature and experienced players.
Liverpool with a new manager and players didn't do at all well last year. But a year on with a team more gelled together, with more idea of the manager's intentions and the difference is night and day.
One of the only times money + new manager has meant instant success was with mourinho, but this was a Chelsea team that went 6th 4th 2nd then 1st with mourinho in his first year. It was a team that was only kept from winning the previous year by an unbeaten Arsenal, that had been growing for several years and had improved drastically the year before. I have no doubt at all that Ranieri would have won the title that year, or any decent manager taking over.
City, PSG, Chelsea, Liverpool, basically every team takes a little adjustment, takes some time to make changes and were significantly improved in the second/third years under a new manager. Should Chelsea be close and in the running, yes, and they are where they weren't in the previous couple of years. That is a huge improvement already, should they be favourites because of spending? No not really. Chelsea have been replacing older players with youngsters in general, Utd will have the same thing happening and will likely outspent most teams over the next 2-3 years as they replace a bunch of players leaving and likely with younger players who can be there for the next decade. That means expensive and expect a few years before the team becomes really great again.
