Small molten salt reactors were actually built. They weren't just paper reactors, even in Rickover's day. Now there are companies working on MSRs for commercial use. There's more computer simulation than running reactors so far, partly because governments are much more cautious now. But I'll also point out that Rickover in 1957 had no idea what computers in 2020 would be capable of.
I think it's reasonable to suspect that we didn't find the best possible reactor design six decades ago.
The part that the computers help with - nuclear and thermodynamic physics ODEs - isn't the hard part. A couple of sharp grad students can do that with OpenFOAM and a modest workstation.
The hard parts are the operations, maintenance, building for robustness, and enormous amounts of empirical field experience with the materials.
Rickover and his contemporaries judged - rightly - that those issues would make MSR and metal-cooled reactors too finicky to be of practical military value.
Maybe we shouldn't base our civilian energy structure on what has practical military value, even if it made sense as an expedient in 1957.
Operations is hardly an advantage of LWRs over MSRs, especially if you stick with simple designs instead of LFTR (as almost all real projects are doing). Those also make maintenance pretty simple. Building for robustness is a lot easier when you don't need build lots of active safety systems or an oversize containment dome due to high-pressure coolant. And some designs use existing nuclear-rated materials.
Only one. She was a contemporary of the Nautilus. It was their experience with that vessel that killed liquid metal coolant for the navy.
It might help to understand something special about the nuclear navy in those days - prototypes in the lab don't count. Prototypes on land don't count either. The only prototypes that counted were ones that actually went to sea. All the way through the Skipjack generation, they were regularly doing crazy-eyed one-off experiments.
I think it's reasonable to suspect that we didn't find the best possible reactor design six decades ago.