Do you have a source for this? Most gas power plants today are combined-cycle [0], meaning they first put the hot combustion gas through a gas turbine as you said and _then_ they use the waste heat to drive a steam turbine as well. This design is responsible for the significant efficiency advantage natural gas generation has over coal. So it doesn't make sense to claim that gas power plants are cheaper due to the turbine technology because most built today use both gas and steam turbines.
The economics of the pure gas turbine vs the combined cycle depends on the fraction of the time it spends running.
For a peaking plant you are only going to run it a fraction of the time so you care about the capital cost and not about the fuel cost... So you're going to use the cheaper to build but more expensive to operate pure gas turbine.
If you are running the plant all day then the economics are favorable to go combined cycle where you start with a gas turbine, recover heat from the exhaust, and feed that through a steam turbine. The capital cost is more than the peaking plant, less than the steam turbine on it's own, but the fuel efficiency is great which leads to lower operating costs. (e.g. the steam turbine in a combined cycle plant is much smaller than a stand-alone steam turbine with the same energy output as the whole plant)
In the case of nuclear it is worse though because you do absurd things: a PWR has "steam generators" which are huge heat exchangers, larger than the pressure vessel, that use hot water at high pressure to boil water at low pressure. For liquid metal reactors the heat exchangers are even larger
https://www.youtube.com/watch?v=JIkYOFxcqRg
Contrast that to the heat recovery units used in the combined cycle turbine that couple hot gases to water or the sodium-to-air heat exchangers that rejected heat from the fast flux test facility. In terms of size these are like a bug splatter on the plans for a PWR.
But I agree, we will want to have CO2 braydon cycle eventually.
China is burning more than three billion tons of coal per year. Now. Replacing coal is not some issue for the 70’s. It’s a huge issue now.
This happens because you're forgetting an important factor: coal is much more available in many regions than gas.
You still hear people compare nuclear costs to coal because coal was competitive in the 1970s. They quit building coal plants at the same time they quit building nuclear plants, for the same reason —- gas turbine generators based on airplane engines have a capital cost about 10% of the steam turbines used for coal and nuclear.
Even if the heat were free and you could burn coal without asking “what do you do with the waste?” you would struggle to be profitable with either coal or nuclear…. Unless you could couple these energy sources to a gas turbine. In the case of coal you need to gasify it (say make hydrogen out of it and pump the carbon underground) in the case of nuclear you need a new reactor type that runs at higher temperatures (liquid metal, molten salt, gas cooled) and a breakthrough in closed-cycle power sets. If it succeeded though you could fit the power plant in the employee break room at the turbine house of today’s LWR.