Therefore, it seems that the relationship between being able to make accurate probability estimates and success in fields that don't specifically require them is weak.

I would still dispute this claim. My guess of how most fields work is that successful people in those fields have good System 1 intuitions about how their fields work and can make good intuitive probability estimates about various things even if they don't explicitly use Bayes. Many experiments purporting to show that humans are bad at probability may be trying to force humans to solve problems in a format that System 1 didn't evolve to cope with. See, for example, Cosmides and Tooby 1996.