The assumption that "the new owners have paid a 5x or more multiple, and the reason they would is if they think they can cut costs and increase prices", is not universal and in many cases quite new. There are many new owners and buyers for which this is not the case. Your local bar, restaurant, hobby shop, gym, bookstore, daycare and others often transfer without the new owner looking to pay a 5x premium and maximize profits. It's only recently that doctors, dentist, veterinarian offices and other high margin social businesses are getting converted to PE.
It's the enshitification of all the existing third places and extraction of social value for profit, because people will tolerate it due to lack of choice and social need.
Right, it's pretty inevitable given the incentives. I think it's made worse by PE for a few reasons. They are investing with relatively short time horizons because they will need to sell to pay profits. So the long term health of the business is of no interest. If the reputation of the business suffers, that's someone else's problem. Compared to an individual investor who is looking long term, they need to retain customers and reputation.
It's the enshitification of all the existing third places and extraction of social value for profit, because people will tolerate it due to lack of choice and social need.