Tbf to Chelsea, they were a top 4 team when they were taken over. Back in the day the top wasn't as fixed as it was now, you had United and Arsenal guaranteed top 2 but the rest were just whoever happened to be the best of the rest. Arsenal might have been title contenders for longer, but I think Chelsea still would have been competing with Liverpool, Spurs for top 4. Moreover, the increased money coming into the Premier League and Champions League would have helped Chelsea maintain top 4 more or less every season. Chelsea did have some financial issues under Ken Bates ownership so possibly they could have done a Leeds United but I don't think there were irresponsible with their spending at the time.
In any case, I've found their rise to superpower less sinister than City's because they were actually a decent team who were taken to the next level. Moreover, the rules were not in place to stop them at the time from spending more than they earned. City and PSG have clearly got around this through various nefarious measures.