Comment by pfdietz
MSRs have some attractive features, but they also have significant drawbacks.
The most pressing is that fissionable material is spread throughout the fluid, so fission and decay of fission products is occurring right up to the edge of the fluid. The walls and pipes containing the molten salt, and anything dipped into the salt, are exposed to unmoderated neutrons. One can shield using (say) graphite, but then damage to that (and soaking up of radioactive materials) become issues.
The Molten Salt Reactor Experiment at Oak Ridge was near the end of its radiation exposure lifetime when the program ended.
Contrast this to light water reactors. These are designed so that no lifetime component sees unmoderated neutrons. There's a thick barrier of water between the fissioning fuel and the reactor vessel wall and the support structures for the fuel bundles. The bundles themselves are exposed, but they are replaced for refueling and are not lifetime components.
> One can shield using (say) graphite
Oh dear god, no. Graphite is a very good moderator, it is in no way a shield. Those two properties are (sort of) opposites of each other. Lead makes the cheapest and best shield. Also, those parts that are exposed to neutron flux stay radioactive for about 10 years. So it shortens their lifetime in the reactor but the waste isn't a big issue.