Why is the nuclear power industry stagnant?

I think you would benefit from reading TFA. It looks at the actual operating costs of current designs and the dropping price of renewables and points out that the fundamental economics of the nuclear industry are not great right now. It also points out that most of the high-priced daytime usage is about to be scooped up by renewables. This may or may not be fatal to the nuclear industry, but it points to the need for substantial innovation or subsidies.

Nuclear power is unpopular because of media messaging. Coal releases more radiation into the environment on average, even accounting for Chernobyl and Fukushima.

Small modular reactors don’t actually solve any significant issues for the nuclear industry. Construction costs are dwarfed by operating costs and the idea that N small reactors with N times as many parts will somehow require less maintenance is wishful thinking.

They very well could be slightly cheaper over the first 15 years, but nuclear reactors are designed for ~50 year lifespans and are really expensive to decommission.

Look at say Palo Verde it’s close to 4GW with a 82.80% lifetime capacity factor, but needs 2,055 full-time employees and that’s the best case.

Energy crises are caused by cheap energy. When energy is cheap people use a lot and stop investing in new sources. The resulting crisis causes high energy prices which causes people to be more efficient and to invest in new energy sources. It takes 20 or 30 years for this to play out. (mid 1970s, early 2000s, current 2022)

Each cycle leaves behind a tranche of books that reprise the last crisis, with the interesting effect that the literature often looks like a stopped clock.

One bit of stoppage is that people still compare nuclear to coal, although coal has been uneconomical in North America since the 1980s. One issue is that a coal burning plant (like a current nuclear plant) has a huge steam turbine that's more than 10 times the size of gas turbines used for aircraft engines and for generating power from natural gas.

It's no accident therefore that we stopped building coal and nuclear plants at the same time. The Amory Lovins "soft energy path" was not a transition to renewables but rather a transition to methane.

There's not just the capital cost of the steam turbine but also the cost of the heat exchangers, if you look here

https://www.nrc.gov/reactors/pwrs.html

the image is roughly to scale and you see that there are multiple "steam generators" that individually are as large as the reactor vessel and are every bit as safety critical as the reactor vessel because a breakage could lead to a loss of coolant accident.

The cost of the heat handling parts is substantial enough that even if the cost of the core was zero and the heat was free the LWR would still struggle to compete.

A reactor that runs at higher temperature using liquid metal, liquid salt, or a gas coolant like helium, could drive a Brayton cycle gas turbine powerset which would fit inside the employee break room of the turbine house of an LWR.

Of course it's tricky: we have quite a bit of experience with liquid metal reactors, and a little bit with other types. The closed-cycle gas turbine however is a work in progress

https://en.wikipedia.org/wiki/Closed-cycle_gas_turbine

Because it hasn't yet heard about Nitinol