Its not theory, the US navy doesn't run gas backup plants on the subs/carriers. Their reactors follow the load, and its not an insignificant variation, since propulsion is on demand and in the case of a sub, likely the largest consumer.
1. they use diesel generators as backup (they need to and it's a safety net)
2. they follow the load but they also pump out unnecessary energy (heat) into the ocean (you can't do that with normal reactors, BECAUSE you don't have infinite cooling water)
3. it's way smaller and the load is way smaller < 100 MW which of course makes load following way way more easier
The fact that sometimes energy needs to be dumped != system cannot be throttled. And a huge number of nuke plants are already on the coast so, they have just as much water as a sub (not that this really matters).
And I suspect size isn't really a factor here, its more about time variance, which I suspect is higher on a ship than its is on the grid. The grid wouldn't be swinging its power usage as drastically or completely as one would expect from propulsion onboard a ship.
This is more about whether its possible to run the reactor at say 50% rated capacity for long periods of time, which AFAIK naval reactors can do, and to a certain extent so can some civilian plants, rod placement controls not just criticality but in the end heat generation, which translates to power output.
