Do cheats profit from their dishonesty? How widespread is it? Are there any studies of this?
Yes, people profit from cheating, perhaps for a long while. But the jobs they enter aren't as cut-and-dried as claiming you are an olympic athlete and it can take a long time for incompetence to be noticed. And incompetence can arise from other things than cheating.
I don't have evidence about studies but would probably question them unless very well designed. What criteria would you use? Would correspondents honestly admit to it? Could you run a longitudinal study and still be able to check back for prior behaviors.
Some people who cheat actually wind up to be competent, also. They might have actually learned something, or taken jobs for which they knew &quot;enough&quot;. Some people cheat once or twice out of panic, but are otherwise honorable.
It is a very complex question. But I doubt that a lot, even a majority, of cheating is caught at the time and those who are clever enough or misbehave seldom enough will get through any gates we might erect. Our processes are designed to discourage the practice, but they aren't perfect.
And, no, I can't prove people profit, but the imperfect nature of the systems and the possible rewards and the panic among students, etc. etc. certainly imply that cheating happens without consequence.

And if you want to assure that cheating doesn't happen, design the course in such a way that it is irrelevant. In particular, in such a way that it isn't necessary to feel that you need to watch people carefully so that they don't. Of course, your evaluation methods are a bit harder to manage in such a system and the things the students do need to require real understanding. Oral exams are probably ideal, but scale poorly, of course. But even in a large, say, calculus course it only takes a few minutes to determine whether a student understands. My old advisor did this, with a line outside his door and a question or two for each student.
My technique was to use projects rather than exams for the bulk of the grade.
It is probably more difficult in the pandemic age, but also more necessary to think harder about evaluation.