A data scientist is an engineer.
What matters is not how elegant your solution is, what matters is solving the problem. And doing it under cost and time constraints.
An engineer is first and foremost, a person focussed on the end goal, above all else.
You've never met a number theorist.
And you've never met a cryptographer ;-)
At best you're talking about a career change, at worst you're talking about a watered-down version of your intended career.
The money is good though, that's true.
Not so much. "Wants" as "Thinks it needs", but even then, the amount of student debt suggests that neither of those are entirely true either.