You're correct that most of the US is in a power market. I'd still call it regulated though. There are some regions like TVA, Colorado area, and BPA that do their own thing, but BPA is joining CAISO's secondary market (energy imbalance) which is a step towards a full day ahead market which does commitment and dispatch instead of just dispatch (commitment and the sharing of reserves is where the majority of cost savings occur).

The other parts of the US participate in either ERCOT, CAISO, MISO, SPP, ISO-NE, PJM, or NYISO which all do commitment and dispatch. ERCOT is a little unusual as they don't co-optimize reserves in their real-time 5-minute market. Each of these markets has an independent market monitor that looks for participant gaming and other market anomalies. FERC mandated this after some heavy abuse in the north east from a utility where the fine was divided up and went to funding the market monitoring groups. Either this group or sometimes the market software itself looks for instances of market power being demonstrated. For example, if you're unit is sitting right on top of a congested area and your offer jumps up a certain percent, the software pushes you back to the approved offer that the market monitor verified is your true marginal cost. So the market is deregulated, but there is still plenty of regulation of a sort.

In a perfect market, yes you would have uneconomical units shut down quickly, but this isn't the stock market and there are many reasons why this doesn't happen all the time. Maybe you need it for capacity reasons (markets have rules on how much you need to reliably serve load or they even have capacity markets) as wind and solar aren't as reliable as thermal generation.