I think this is actually a water-tight reason: if mathematicians (or any disciplined scholar) wishes to actually contribute to a growing body of knowledge, then they must necessarily take up historical topics.

I don't think this makes much sense. It's not like 'growing bodies of knowledge' are free-floating sets of propositions, and new propositions get thrown into the set every time somebody discovers a new fact for the first time. It would probably make more sense to think of bodies of knowledge as relative to communities. If, for example, civilization got wiped out in some kind of apocalyptic event, and our ancestors had to rediscover basic physics 500 years from now, I think it would be ridiculous to say that those future inquirers weren't contributed to a 'growing body of knowledge' simply because they were retreading territory that used to be known.

I'm all for people investigating history to find old, forgotten ideas that deserve renewed attention. In fact, I think history is especially useful because, by reading thinkers from far removed time periods with different background concepts and presuppositions, we might encounter approaches to problems that wouldn't likely occur to someone only familiar with the current state of the field. But I think it's too strong to say that anybody who wishes to contribute to a growing body of knowledge needs to take up historical topics.

Also, I think it's interesting that you initially pointed out the mathematicians; I would expect mathematical logic (i.e.: set theory, proof theory, model theory) to be the branch of logic that is least likely to benefit from medieval logic.