Private equity snaps up disability services, challenging regulators

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?

No. Private equity means investors who buy equity in non-public companies. That's it. (It used to imply leverage, but that distinction has blurred away.)

In popular discourse it's close to a meaningless term.

You are technically right but I wanted to understand the bigger reason of why this happens:

A company runs well. But then they sell to a private equity. The quality goes down.

This is the common critique against private equity.

Many private businesses "leave money on table". Private equity then acquires these and aim to extract maximum amount of value. Leaving money on table is probably general good. Like employees are reasonably paid, customers aren't charged maximum they can bear. Quality is not lowered as low as possible...

But ofc, if you pay for a company based on not leaving money on table calculation or bet on doing that later all those will change.

Then there are also the actually struggling and dying off companies. But I do not believe that is every one that is being acquired.