Re your comment on CS PhDs not having probability background -- do you find that's true of ML researchers? I would understand that in a bunch of CS specialties, probability may not be a requirement, but in ML I would have expected otherwise.
As a case study, I did most of my grad work on solving Bayesian inverse problems using probabilistic programming for applications in engineering, which is pretty cross-disciplinary. I now work mostly in ML, but I didn't really even touch anything in the ML domain until after I finished school. I could have, the courses were available, but they just weren't relevant to me at the time.
Edit: I wouldn't be surprised if there was a considerable userbase in industries like finance, but in my experience those folks don't share much.
Which largely counts as strong Linear Algebra and Probability Theory background.
CS only comes into the picture at runtime. ML theory is divorced from computability until then.
You don’t need a professional license to do math. Lots of computer scientists to harder and more interesting mathematics than their peers in the math dept. In that respect at least, the main substantive difference between the fields is about $40k/yr.
You're just stating things without justifying them.
What else would you consider a subfield of CS? Finance? Accounting? Logistics? UI design?
What is or isn't a subfield of a given science has nothing to do with the professional qualifications of those who practice it or how the tools may be implemented. We don't call pharmaceuticals "a subfield of robotics" because of how the factories are built.
The same can unfortunately be said of many "statisticians", who use statistics as a big recipe book without understanding the first thing about the mathematical underpinnings of the topic.
Don't believe me?
Go ask the first statistician you run into to give you a half decent explanation of how the Chi-squared distribution and the Chi-squared test works, see what happens.