> in order for the company to be sold at a higher price than it was bought, it still has to be good/better at what it is supposed to be doing

As someone who has worked for PE owned companies I can confidently say that unless you consider the thing they’re “supposed to be doing” to be reflecting profit on the books, you’re wrong.

The PE owners of companies I worked for pushed EBITDA over anything else and as a result our product became a leaning Jenga tower of half finished functionality combined with unfulfilled promises to customers. Foundational systems were completely neglected in favor of whatever kept costs low and increased closed ARR focused deals. We sold for many times our previous valuation and not one person I spoke to in the company itself or our customer base felt the product was better, all agreed it was worse.