What? The market will not go out of business. Capital is relatively plentiful and there are many participants, many trying to geologically diversify. No economic plant will stay shutdown for long. The sooner uneconomic plants shutdown the better. That was the main point of power pools...
What you describe might happen in areas still under rate base. Fortunately most power pools have been running for a decade now (without the drama we saw in CA). Only areas where the 'local' power companies have so much power (cough, Southern Company, cough) that market based systems are being delayed is bankruptcy and bailout still a possibility.
The fundamental flaw in your argument is that you assume that uneconomic plants are not needed. This is far from true!! For the 1-5 hottest days of the year*, uneconomic plants are desperately needed when the rest of power is already used up. There are plenty of sites across the US which operate for less than 2 weeks a year, because they are for the greatest "peak of the peak". The power grid needs these plants just as badly as it needs the 24/7 coal/nuclear plant. But in a pure economic model, those handful of days a year aren't enough to justify maintaining that kind of plant. Speculating that the price will skyrocket on hottest of hot days enough to keep you solvent is very risky. It is also bad for society as a whole- society risks not having enough power AND is assured of higher electricity rates on hot days.
In the old days, the utility would operate such plants since they relied on them. Nowadays, there are 2 kinds of power pools- those which subsidize this kind of plant and those which do not. In subsidized markets, they are paid a capacity payment every day which they are "ready". This kind of "payment for nothing" gives free-marketers heartburn however, so some markets don't do this, or don't do it as much as they need. Those markets are the ones which have huge problems on the hottest days, and because they are frequently on the edge of overcapacity, the price of electricity is always higher.
Keep in mind that "idle plants" is a synonym to "overhead which isn't making me money". Private industry wants to keep the % of idle plants as low as possible.
In regulated markets, the utility has the obligation to do what is best for their customers. It is better for their customers that the grid isn't near the edge of overcapacity on a daily basis. Their % of idle plants is higher as a result. With a larger pool of potential power available, the utility can use the cheapest generation on the majority of days, and keep the expensive power plants as a reserve for the very hottest days. The private industry model thinks those reserve plants are uneconomical, and so on the hottest days they get into trouble.
For the end customer, private electricity markets will always be less predictable compared to a regulated market. Usually in a way which is not favorable to the customer.