Is it correct to understand private equity as transferring service quality to the initial set of customers (who were subsidised) from the new customers who have to give up quality to make the whole venture feasible?
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In popular discourse it's close to a meaningless term.
A company runs well. But then they sell to a private equity. The quality goes down.
This is the common critique against private equity.
I'm sceptical this pattern is true. But because of the aforementioned ambiguity in terms of what constites private equity, it's an essentially unanswerable question.
If you want to support the hypothesis, you focus on investors who use a lot of leverage (LBOs) and those who focus on distressed assets. There is reason to criticise the former, which often amounts to limited-liability arbitrage. The latter is just sampling bias.
Similarly, if you wanted to reject the hypothesis, you'd include venture capital in private equity, as well family offices that quietly collect businesses in an area they've long operated in, but want to say they're in private equity versus the family restaurant-parts supply business or whatnot.
Going back to something like disability services, I don't see it being run phenomenally better by a VC or family or public company. The problem is fundamental to the profit incentives of the industry. Not the fact that the owners brand themselves as private equity.