Essentially. The CO2 cooled AGR has much lower power density and was thought by its designers to be a much superior design to water cooling for safety and cost reasons.

It turns out, definitely not on cost grounds and the AGRs are all reaching technical end of life a few years after their original rated lives whereas light water reactors are getting life extensions basically everywhere for decades beyond that.

Light water thermal reactors are the worst kind of nuclear reactor except for all the other ones which have been built.

The uranium has to be in a small volume for the chain reaction to work.

That doesn't mean the power density has to be high.

It has to be high within the core. I suppose you could add some empty space nearby

No, it does not have to be high within the core. A reactor can be operated at a low power level. This is not like a fire that goes out if the flame is too weak.

The problem with that is that cores are very expensive. They require 100s of kgs of enriched uranium. If you run them at half power, you need twice as many and your cost goes up dramatically.

The uranium lasts twice as long, though. So aside from interest costs it's a wash, at least for fuel costs.

You are right that the reactor structure costs more. Which is the point I've been trying to make.