I think the root of this problem is that private equity managers often have no skin in the game and tend to fail upward. It would be one thing if a private equity manager had a record of taking a company private, streamlining it and making it sustainable for decades to come. Even with the human cost of that, it's preferable to a company going prompt bankrupt. But too many managers seem to take these things private and then run them straight into the ground. Toys'R'Us, for instance, or Red Lobster as quoted in the article. In the latter's case, the management tried boneheaded promotions like "unlimited shrimp," which would be a bad idea even in a zero interest rate world.
I'd propose instead some sort of mandatory filing on the part of private equity managers that is publicly accessible and searchable and shows the track record of a private equity manager, with links to all of the other managers they've worked with. Then, when a PE investor proposes to take a company private, they're required by the SEC to demonstrate that their management isn't tainted by a chain of incompetence.
Who knows if that would work, but it might increase the skin in the game somewhat. The status quo seems to be HBS grads performing with mediocrity at best and having no real accountability.
The most broad brush would be a complete and total ban on mergers and acquisitions, an idea that I find mildly interesting but I suspect would fail in practice. Perhaps M&A could be restricted somehow, with particular criteria disqualifying one from being able to accquire?