There isn't a but here; resources determine literally everything. Before a ball is even kicked going into a new campaign, resources will determine how you approach the transfer window and preseason and what level you can stress a squad to in preparation. The more resources, the greater the landscape is altered, especially in terms of risk and jeopardy.
Pep can do things he's hailed for because of his resources. His squads don't have to go all out, high octane from the start of a campaign to the end of one, like those rivalling City since he's been there have to because the load they share gives tremendous advantages in terms of recovery and opportunism. His squads are by far the least likely to flag at any point in a campaign.
some of the reduction in vulnerability is still down to Pep's approach as well. His style, particularly in league campaigns, is one that tries to eliminate jeopardy as much as possible through retaining possession and choking opposition. It's seems more sustainable and less taxing than something like Klopp's style over the long run over a season and from year to year.
We're talking about these other managers extrapolated at their best. In every case, those teams overseen by these other coaches could take their foot off the pedal because of the dominance they exerted. It manifested in different ways for different coaches, but it was clear when they were at the top of their game. We would play kids and the subs rather than try and rack up absurd goal or points tallies; Mourinho would just shut up shop and iron bolt games; 1 or 2 nil up and most games were pretty much over. Wenger's lot started trying to score the greatest team goals mankind had ever witnessed. You give anyone of them unheralded resources and what they always were is extrapolated, just like it is for Pep.
I think what is forgotten is that Pep does not have the blueprint on success and his unprecedented points totals do not signify what people believe they do because they have only become a thing in his time because he's made it so where other managers focused on what was important to them: SAF - rounding out his players and giving his squad as much playing time as possible for them all to be sharp and able and also to develop; Mourinho - his ultimate aim would probably have been to set the greatest defensive records known to man and probably also to target GD.
We became much more points focused because of Mourinho, but still tried to retain SAF's principles wherever possible. Take that squad of competent subs and replace it with a monstrous rotation and things change, significantly.
You've mentioned Klopp and my thinking is, all of a sudden, he has considerably more means to play his high octane football, rotating in players of similar quality who can maintain the output of his starters, just as with Pep, he suddenly can observe the landscape differently and take far more risks with his charges as jeopardy itself and consequence for doing so lessens.
I don't think there's an issue with character when it comes to the kind of money on the table.
Also in terms of squad composition he is intentional about recruiting or coaching up versatile players that can capably deputize is multiple roles or positions (except Rodri's), making the team overall less vulnerable to shocks from key injuries. In this current squad, you only really have Kyle Walker and Haaland who can only do one role effectively. The rest can do the mixing and matching. Even Ederson can play striker (jk). That is down to their quality and adaptability as players, but also the coaching. Pep intentionally keeps the squad on the smaller side in order to better manage it. Other squads are usually bigger in terms of sheer number, not quality.
However any of them composed a squad is up to them. The means and personnel to do so is what's important. Optimisation is the crux and with the greatest of resources comes the greatest chance to create something bespoke and perfect for how you wish to do things. It cannot be understated how cushy an advantageous that is over a league campaign. We often display Fergie's squads because it needs to be highlighted to show the discrepancy and brilliance of the manger that he could do what he did with what he had at his disposal; for the major body of his managerial career, his squad players would not be starters at the top clubs, and the moment we did have that, points tallies, unsurprisingly, went up despite the fundamental principles being adhered to in the same way.
You would also need to factor in other aspects of management like man management and squad composition. It's not a given that Klopp's lovey-dovey, against-the-odds, loyal-to-a-fault, we-are-family style would work just as effectively if you throw even more egos of starter-level players into the mix. You already see cracks with Nunez and Salah this year now that Klopp is leaving. I think SAF and Klopp have excellent gravitas, so they could likely pull it off, but it's not a given. With Klopp, I have often wondered if it's a chicken or egg problem with the injuries. For a while, I thought Liverpool were working within financial constraints and chancing it by taking punts on cheaper players with spotty injury records in the hopes that they could turn in around at Liverpool and represent value transfers (Thiago, Konate, Ox). But then you have guys like Matip, Keita etc, that make me wonder if there is something about Klopp's approach that makes players more susceptible to injury, thereby increasing the vulnerability of the squad. And this is only the physical side of it. The constant emotionalism and last-minute comebacks have to be pretty mentally draining as well.
As above, I just don't see this as a factor for any one of the managers. With endless resources, squad composition can be so custom-built and perfect that harmonising isn't going to be difficult, and what's more, those same resources ensure you can throw away anything you like and simply bring in the next one, no bother whatsoever. It doesn't take much of that to strike gold. The equivalence in real world for Pep would be: what happens if he's lumped with those FB's and CB's he cycled through and had to use them, faults and flaws all? Is he still playing the same brand of football or not? The guy gets to tweak and tweak and tweak until things are how he wants them. Not even Mourinho could do that under Abramovich. It's something beholden only to Pep and he's comedic resources.
Mourinho has had amazing squads and yet he always burns out everywhere. Man-for-man, I would have Mourinho's Real Madrid squads over this City squad. City have a great squad, but a lot of the names are also just kinda "meh" relative to the hype the squad gets. Discussions of these otherworldly, "two first eleven" City squads used to include guys like Sterling, Jesus and Zinchenko and now they are all pretty much afterthoughts at their new clubs even though they are still prime age.
This is relative, and relatively, he was up against Barcelona. He amassed crazy points totals and actually did very well with what he had, just that he was thwarted by the team most put up against 89-93 AC Milan as the literal best club side of all time. Pep has had no such opposition in England.