Most electricity and infrastructure is profitable. But not after carving it out in a way that looks at it in complete isolation. Just like train infrastructure creates a lot of business around the area of the train infrastructure, even if the train itself may seem not self sustained.

I'm fairly sure that the total economic value that we get out of roads far exceeds the cost it takes to create and maintain them, yes. A similar argument can probably be made for justice systems and armies.

If a power generation system costs more to operate than the value of power we get out of it, it's probably not very useful. I think that's what we're talking about here.

Why would we choose a more expensive form of energy rather than cheaper forms?

There are good reasons to choose more expensive things, but "nuclear sounds cool" is not a good reason. There must be some sort of rationale and benefit beyond that.

It does not. But there are so many sources that can be. And easily at that. So why go this route?

Those things you pay for indirectly via taxes. Electricity you pay for directly. you can build unprofitable economically uncompetitive power, like nukes, and your rates will go up. People tend not to like that, but you can do it.

Not sure about profitable but the lower the cost is the generate electricity, the better off the world will be. Cracking energy is, to state the obvious, a huge unlock.

Because in their wisdom the politicians have created energy markets.

The costs for generating electricity needs to be paid for somehow.

Having the consumers of the electricity pay for has a lot of advantages!