I think looking to CompSci is the right move, but I still don’t see many folks discussing computational complexity as a real, mathematical limit.

I think this viewpoint depends on assuming that math is primarily computation. I think our education system and stories reinforce this misconception. But another fundamental component is creation. People created axioms (eg. ZFC) as a foundation for mathematics, then they chose and named almost every mathematical concept based on that foundation. Sure, there are "computations" in some vague sense, but not in the sense of computation theory. Importantly there is no right answer. People have invented alternative systems and will continue to do so. But I haven't seen a computer compute a better computer... Anyway I agree that computation is underrated especially in terms of proofs (see recent math competition). And increased computation has allowed for breakthroughs. I'm just saying the meta framework of creating the system, defining the terms, and choosing the computations is also a huge factor.