IPOs also kill a lot of companies. Now you have a new list of investors you are obligated to attend to, and what those investors what is not always to make your company more successful, if it can make more money now.
Not just the IPO. Being public at all subjects you to the perverse and destructive incentive of needing to maximize shareholder value. Just because some private companies take VC funding (and subject themselves to analogous forces) doesn't mean that's required or expected.
So keep the profits only for the rich then? I rather see more IPOs for the rest of us.
The reverse is much more true. When private equity takes a public company private, there's a 50% chance they'll kill the company.
Also, private companies fail at a much higher rate than public ones do.