The idea that there's a "fair" market left in the US is an abject joke. At BEST, there are a handful of companies divvying up a market collusively. At worst, and increasingly commonly, we have effective duopolies that juuuust skate the currently en vogue legal definitions to create 2 different walled gardens. Name for me a market (of financial significance) which isn't currently dominated by two mini-monopolies, and I'll show you a private equity firm which is leveraging its ass off to try to capture it, and make it so.
There are many such markets -- real estate, construction, financial services (banking, mortgages, credit cards, etc), agriculture, retail (no, walmart is not a monopoly), oil, automotive, air travel, I can name many more.
The only big national industries that are dominated by monopolies I would say are telecommunications, utilities, silicon, pharmaceuticals, rail, and even most of these have a few more companies than two. Granted, 3 telecoms is not much of an improvement over 2, but nevertheless your claim is broadly speaking false.
Are there private equity firms trying to consolidate? Sure, but in any of the above they haven't really met with much success.
It's funny that your first example is real estate, when I've read many stories this past year about how private equity is buying up lots of residential homes, and driving the prices even higher than what inflation accounts for. It was a huge story recently that Zillow was trying to buy (and flip) homes, based on their pricing algorithm. Thankfully, they failed miserably.
Absolutely. I would go so far as to say healthcare is essentially operated by regulatory capture given how deeply the Medicare market leads where the rest of the market directionally goes.