Its obvious very important but Chelsea won 2 league titles while United and City both had much greater resources into the current side.
Chelsea seems like a very odd example to cite!
Chelsea have won more in the 15 years that Abramovich has taken over than the rest of their history combined. They didn't win the league for 50 years before Abramovich bought the club, and only once in their entire history at that point; since he owned Chelsea they've won the league 5 times. Plus, they've won the Champions League, the Europa League, the FA Cup 5 times, the League Cup 3 times, and won 2 major trophies in a season on four occasions.
This is despite the fact that in this period they've been managed by Mourinho, Grant, Scolari, Wilkins, Hiddink, Ancelotti, Villas-Boas, di Matteo, Benitez, Mourinho, Holland, Hiddink, Conte and Sarri. They've had zero stability or structure, but it hasn't mattered at all because the money has kept being pumped in.
Now even they are struggling to compete at the very top table, and to match the investment of others. That is the climate that exists now. It's a completely different climate compared to when Arsenal were winning the league.
You see issues and problems in the back office that were causing problems at Arsenal. But none of those things were perceived to be problems when Arsenal were perceived to be doing well. They were only raised as issues when finishing in the top four, winning the FA Cup, and making the Champions League knockout stages was deemed unsatisfactory.
The reality is that the structure and approach of Arsenal and Wenger probably had nothing to do with why Arsenal's level has declined. And when they were at that level of regularly finishing in the top four, etc, far from being disgruntled, supporters should have recognised that it was the best that they could reasonably hope for with their budget and investment.
Pochettino is continually lauded as a genius, but that's because the level of expectation at Spurs is so much lower than Arsenal. Because they haven't had that period of being a powerhouse club that wins the league, has a great team, and can compete with anyone in Europe. Undoubtedly, Pochettino has done a great job, but it's all a case of perception. He hasn't done measurably better than Wenger in his so-called lean years, in fact he has arguably done worse as he has won nothing for Spurs.
If Arsenal under Wenger had lost 1-3 at home to Wolves, as Spurs did the other day, he would have been absolutely hammered. By both fans and media. I doubt Pochettino will experience such criticism, and will remain favourite to take over at Man United and possibly Real Madrid.
But where Spurs are now is the best that they can reasonably hope for. They won't win the league. Eventually this team will break up. And they won't have the budget to rebuild it. They have been lucky that they got Ali for £5 million, while Kane came through their youth system. That's £300 million worth of players for next to nothing. When they have to replace them, they won't be able to do it with £5 million. When Eriksen goes, they won't be able to replace him with another midfielder who costs £10 million. They're going to be in exactly the same position Arsenal were in when they were selling Cole, Henry, Vieira, Fabregas, Nasri, van Persie, Sanchez, and many others.
And then, on top of that, Arsenal have the disadvantage of the owners not really caring about results. They're not really bothered. It's just a cash cow for them. So they would struggle to compete anyway, but this is obviously hamstringing them considerably.
You might have to go through 5 or 6 managers before this dawns on many Arsenal fans. We're Arsenal Football Club! It's not good enough! Unfortunately, that doesn't mean anything any more.