The idea of a management buyout is that the people who run a public company pay a premium to buy the company, then try to make it worth more money by running it better as a private company than it was run as a public company. You see the problem. They're already the people running the company. If they could run it better, they should just run it better. If they have ideas for things to do to make the company worth more money, they should just do those things. That is literally their job. They are paid to do that. Why should they hold back on those ideas until they own the whole company themselves?
There are various answers to that question, but the only really satisfying one is: It's a free country. If the managers think they can do better without the shareholders, and want to pay a premium, and the shareholders are willing to sell, then go right ahead, whatever. But because everyone realizes how weird it is, the Delaware courts -- which tend to make all these decisions -- have built up a bunch of protections to make sure that the negotiations are as fair as possible. Generally, the shareholders need to be represented by a committee of independent directors, and the managers who want to buy the company have to be honest with the directors and the shareholders, and then it all goes to court and a Delaware chancellor takes a good hard look at it and makes sure it doesn't look too bad.