The thing is that tax on such businesses are too low. Same as it is happening on other areas, the negative effects to society have zero counter measurements.
AI will take all work and the government will crash because lack of money? Who cares?
Private Firm buys all houses in a region and force the market into a false sense of scarcity to inflate prices? What could possibly go wrong?
Other companies being bought in bulks by big players to hold IPs while dismissing all employees with false pretense that they are losing money? Nothing to see here..
The fact that the cost of using gray area to hide and move money to not pay taxes has a predictable and slow movement is the best for those players.
Back then (even in Reagan's 1980s) the Michael Douglas character types were despised by society. Now they are emulated and mainstreamed. We are set to have more private equity than McDonalds. American Capitalism is all about capital extraction now, not value creation.
The point is short-term profits. The private equity firms vampirically suck a lot of money out of these companies as they ruin them, and keep the money they steal.
Arguably they shouldn't be allowed to exist: They use what seem to be loopholes in corporate law to run what are essentially embezzlement schemes. If a lone person runs an embezzlement scheme, that's possibly a felony charge. It shouldn't be a loophole that a company can do it just fine without repercussions when we know a lone individual doing it is a crime.
The two problems in why they are allowed to exist are enforcement and probably legislation. Legislation is needed to close any actual loopholes in the law and/or just explicitly say things like "Leveraged Buy Outs are illegal". Enforcement is getting courts to see this as a crime and prosecute it as such. They may be waiting for legislation before they feel confident enforcing it.
Fixing those problems is certainly easier said than done.
(ETA: Also some of this is classic Anti-Trust violations. Trusts/Monopolies are still illegal. Enforcement has been somewhat negligent in the US this century and some of these deals cross too many country borders making enforcement in general harder. In this specific case, a US private equity firm buying a Japanese company, who enforces the anti-trust issue, especially if the Japanese company was already a de facto local monopoly before joining the international one?)
They exist as a consequence of how company ownership works (i.e. that it can be bought and sold). You would need to figure out some quite specific wording to prevent this without also preventing all kinds of other kinds of transfer of company ownership.
In principle, private equity firms could be a net positive: they could take over a business that's failing or just not living up to its potential, and turn around the management of it to improve it for all concerned. They often market themselves on this concept. In practice it rarely seems to work this way, where either they fail to make any return on their investment or they basically do this kind of monopolising, short-term extortion of customers. Often both.
(Patrick Boyle has a video on them from the financial side if you want some details: https://www.youtube.com/watch?v=bfUOPDOLHvE TLDW: they often aren't a great deal for investors, either)
Buy a great company, suck as much cash as they can before discarding the empty carcass.