First off, I have no interest in being a mathematician. Math was always and continues to be quite difficult for me.
So, as an outsider to advanced math, it blows my mind that there are people who’s entire job title is mathematician. How does that work? What does a mathematician do?
I don’t know a lot about other fields but stat people are hired a lot by research institutions. A good statistician can reduce the number of experiments you need to do, being able to test a drug/treatment with 7 people instead of 100 means a lot. They save a lot of money.
Also being able to make inference from past data, incomplete data, use correct math (there is always different ways to solve things) so they don’t make mistakes.
And a lot of people with stat degree join either academia, or other fields that have actual problems and use their background to solve issues.