My view is that some degree of technical facility helps a lot. As I recently wrote, I think that learning to read very carefully and not make unwarranted assumptions is a very important skill, and one way to get it is by studying proof-based math. I don't have strong views on how much studying pure math and TCS help after the first 1-2 years. I think that the case for learning advanced statistics & machine learning is much stronger.

Separately, I benefited a huge amount from reading and interacting with elite mathematicians. Even though they weren't thinking about the things that I'm doing now directly, I was able to transfer what I had learned from them to the things that I'm currently focused on. That's the peer group effect.