I think the theory is that they buy up a significant portion of the market, i.e. consolidate lots of independents. Then they raise prices in concert, and take advantage of reduced competition.
Wouldn't that create a good opportunity for people to start new pet cares, and undercut the presumably overprized PE-consolidated chains? Pet care doesn't seem to be highly regulated or have other high barriers to entry AFAIK.
PE seems to do well in industries where consumer choice has a good amount of inertia, where it's a pain in the ass to change providers - anything that's at least partially trust and reputation based and where people order to lock in a choice and sit on it.
Basically, they're liquidating built up customer goodwill.
Barrier to entry is high, is pretty capital intensive to setup a large enough childcare facility that takes appropriate advantage of child staffing minimums.