You do realize that iron would become brittle as steel from the neutron flux if you built your reactor vessel out of it, right? It's a vague problem with fission reactors that required some procedural adjustments once neutron embrittlement was better understood, but with orders of magnitude greater neutron flux...
Nor can you rely on a isotope chart of a single element to predict what's going to occur in a high neutron flux environment.
For example, Fe 58 is stable. Capture a neutron it becomes Fe 59, with a 44 day halflife to Co 59. If Co 59 captures a neutron, it becomes Co 60, which is a long-lived radioisotope.
So I guess you do get a reactor vessel with a certain amount of cobalt isotopes, no?
I wouldn't classify this as an "unsolvable problem" but you can't magically wave your hands and make them go away.
For all the "oh my god radioactivity" crap that's going around, the simple fact of the matter is that you can access the core of a fission reactor while it's online whereas you cannot access the core of a fusion reactor while it's online.