Whatever happened to HTGRs? I recall people speculating that this type of reactor would go into PLAN SSNs since the 90s, but nothing seems to have ever materialized...
Too exotic and high risk. The plant itself however have promise. it allows much higher temperature to be attained, no pressurization needed so there is potential to use Superheated steam instead of typical PWR saturated steam.
It is also possible to entirely replace steam turbine with Brayton cycle (essentially, yes a nuclear gas turbine) But yeah too exotic.
It also promise much lower weight per Horsepower. As compared to PWR, no need for extra pressurization or secondary loop.
DARPA studies on alternate Submarine reactors, for CONFORM program which, got killed by Admiral Rickover. The DARPA studies
promised following :

Notice that HTGR and LMCR (Liquid Metal Cooled Reactor) offers low specifc weight for every horsepower generated. Thus the plant can be smaller, consume less volume and in turn allow smaller submarine or extra volume to be allocated for something else. 40000 SHP HTGR plant for example will be about 858 metric tonne, compared to 1523 metric tonne for PWR plant. LMCR plant is heavier at 1013 Metric tonne but not as heavy as PWR one.
The calculation is based on "Theory of Submarine Design" and Norman Polmar's "Cold War Submarine" book. and cover typical reactor setup
PWR itself are chosen mainly because it's working, scalable, large experience exist, it use water which easily procured. But when time comes for lightweight reactor or higher thermal efficiency, one can consider going HTGR or LMCR. Typical PWR plant due to its dual loop (primary and secondary) can only achieve typical efficiency of 33%. LMCR and HTGR can be higher as there wont be need for pressurization and primary loop.