I wonder if it's possible to run it hot enough for the radiation damage (basically a bunch of dislocations, right?) to just anneal itself out continuously, like how Wigner energy is dissipated in graphite when it's hot enough.
No, this is fundamentally impossible with steel. Annealing works by making the material more "plastic", and this necessarily reduces its tensile strength. Which is the limiting factor for the vessel.
You can make the vessel thicker to compensate, but then you can just make it thicker in the first place and skip annealing.
