Modern reactors are capable of load following, although I suppose that comes with some wear and tear, as with any process. So it is always going to be better to run them full tilt and covert the excess to hydrogen.
In the 60s a reactor called the SLOWPOKE was developed in Canada by AECL. I believe its power output was in the 10s of kilowatts for the early ones which they then increased to a few megawatts for use as a district heating. They were passively cooled, used light water, and had several other inherent safety features, such as the reaction slowing if the water gets too hot or forms voids. They were designed to run unmanned.
Despite meeting all their design goals, they didn't sell many, so they are mostly used for research.
Presumably their power generation wasn't particularly cost effective, just as we're seeing with the mature nuclear industry in the United states?