I think if you want to make good money, then your realistic options are finance, crypto or AI.
I would pick AI, because it's a growth industry with on-going innovation. You would also be able to work in many different kinds of applications. It seems like it would be fulfilling work.
You didn't mention why you're uncomfortable with trading. Finance used to be a great choice, but it's not a growth industry now, innovation stopped after the Financial Crisis in 2008, and the industry has been saturated with PhDs for over a decade. Meaning math PhDs not in demand very much anymore in finance and most of the work is not very interesting anyway.
Personally, I wouldn't pick crypto ("blockchain") as a lifetime career.
Note that any of these career would require significant effort and learning on your part. You didn't mention what your PhD in mathematics is in. You would be competing with PhDs who have done their thesis in something highly relevant to AI or finance and/or have done a great deal of research on the topic before applying for jobs in their target field.
If you don't care about how much money you'll make, and enjoyed your PhD work, then I suppose postdoc would make sense. If you don't care about money and didn't like the academic environment, then you could go into teaching relatively easily with your qualifications. Perhaps teaching / lecturing at a private school or college, if not a university. I would suggest that you do care about money though, because it is an important factor in determining your quality of life.
Re. uncomfortable with finance: I guess it's a mostly "intuitive" ethical concern.
I don't feel like finance is very much part of a society I'd like to live in or contribute to.
I have heard arguments that e.g. trading is a big part of making the economy fluid and optimizing throughput or something, but it sort of rings wrong to me.
Maybe it's just preconceptions and I should learn more about it!
Re. significant learning: Indeed, and that's part of the problem: since I'm not entirely sure where I want to go, I don't really have the mind to invest too much time learning about fields I probably won't work in, which makes my profile less attractive I guess.
I originally had hopes that I could learn on the job: you often hear people tell you that a math PhD is proof that you can learn efficiently and have the capacity to work any technical field, or something.
But I see now that it's probably not how it works: hirers still want some proof you're competent in their specific field.
Re. postdoc: the problem here is that the competition is rather fierce and the work conditions not always optimal.
Your intuition about ethical dilemmas in finance is not entirely misplaced. I know all the arguments about finance and trading being useful because it is the process by which capital is "efficiently" allocated in the real economy, but that's academic fantasy which ignores how the real world works. The truth is, in order thrive in finance (and, by extension, crypto) you need to be someone who is perfectly happy being "ethically flexible."
By the time you start running into these ethical dilemmas, you're typically in too deep and it's too late to get out. You justify it to yourself because you're just a small cog in a big machine who can't change anything and you need to earn a living (and have gotten too dependent to a certain level of income that you can't earn anywhere else at that point). You can relatively easily make as much as a doctor or lawyer, but I can assure you that in a successful finance career you will need to "ethically flexible" whether you like it or not. A doctor can go home knowing that they saved lives, in finance you'll feel the pretty much the exact opposite.
You said the competition for postdoc is rather fierce, the competition for other jobs (e.g. AI and finance jobs) is just as fierce if not more. Basing your decision on fear of competition is not a good idea because every career or job is highly competitive.
You need to pick a track and work on it. Significant learning is part of it, but I should also mention that your network is equally important if not more. You need to build your network. One way to do this is to stay in touch with people you went to school with, not least because some of them will get jobs in your target field, and they might be able to help bring you onboard. Another way to network is to ask out people you don't know (e.g. that you find on LinkedIn, or profs or whatever) for "coffee" to learn about their industry - this is known as an "informational interview," you can Google the term to learn more. Good luck!
I would pick AI, because it's a growth industry with on-going innovation. You would also be able to work in many different kinds of applications. It seems like it would be fulfilling work.
You didn't mention why you're uncomfortable with trading. Finance used to be a great choice, but it's not a growth industry now, innovation stopped after the Financial Crisis in 2008, and the industry has been saturated with PhDs for over a decade. Meaning math PhDs not in demand very much anymore in finance and most of the work is not very interesting anyway.
Personally, I wouldn't pick crypto ("blockchain") as a lifetime career.
Note that any of these career would require significant effort and learning on your part. You didn't mention what your PhD in mathematics is in. You would be competing with PhDs who have done their thesis in something highly relevant to AI or finance and/or have done a great deal of research on the topic before applying for jobs in their target field.
If you don't care about how much money you'll make, and enjoyed your PhD work, then I suppose postdoc would make sense. If you don't care about money and didn't like the academic environment, then you could go into teaching relatively easily with your qualifications. Perhaps teaching / lecturing at a private school or college, if not a university. I would suggest that you do care about money though, because it is an important factor in determining your quality of life.