PSG, City & Chavs(*) aren't in it to make money... It's about prestige and sports-washing (see current discussion elsewhere in thread)......
So, put yourself in the shoes of Qatar or Abu Dhabi. What those kingdoms have been desperate to do for decades is diversify their wealth and asset portfolio beyond just oil extraction, both due to the economic problems caused by price fluctuation and the knowledge that one way or another that market will eventually end. This isn't armchair psychology, this is the constantly expressed guiding ideology of these governments.
This is why Dubai is a gleaming tourist mecca subsidized by state-owned luxury airlines, this is why they're always partnering with American and other foreign Universities, this is why MBS in Saudi Arabia is always coming up with hare-brained schemes, it's all about establishing sources of state revenue that are not oil-based. Money is no object now, but they need future dollars, their opportunity costs and incentives are different than a western investor.
These are also, as we know, deeply authoritarian, brutal, and corrupt regimes. They are badly in need of guillotine insurance, so to speak. And their population is among the most football-obsessed in the world.
Investing in European clubs solves both problems! The "sportswashing" to the extent "look at our shiny winning football team a continent away" is part of the motivation isn't meant to influence Europeans, it's meant to influence their own people.
Two very obvious things that reveal the sportswashing narrative to have no clothes are first that these projects have brought more spotlight on the awfulness of these regimes than anything in decades and everyone hates their clubs, and second that the existentially important ally of these regimes is not the European voter but the American military-industrial complex, which recent positive trends notwithstanding doesn't know or care the first thing about football.
The sheikhs are in this to create a sustainable revenue stream that isn't oil-dependent, and they, exactly like ENIC, exactly like the PL American contingent, all see the top of European football as an undervalued future growth market, based heavily on the potential to transform into an anti-competitive NFL of Pan-European Football. Their underlying imperatives and motivations are different, but they are in football to accomplish the same goal and they understand one another as allies, not competitors.
(Abramovich is fundamentally all the same shit, just with slightly different particulars)