That's the opposite of what happens with PE. PE firms don't buy fairly priced, well run businesses. They (typically) buy underpriced, poorly performing but cash flow heavy businesses that would benefit from leveraging up and making operations more lean.
Think about it, if a business is fairly priced and well run, PE firms have no incentive to buy it because where do they generate returns?
I don't like PE firms but there's no doubt that they force businesses to operate better, and ultimately that benefits people like you and me who have retirement savings, because PE firms aren't getting their money out of thin air.