I don't think I really disagree with you with respect to becoming an expert, but what you think of as becoming an expert may be different from what others are thinking.
Personally, what I see is a lot of AI becoming commoditized. There was a time when you had to have a fairly strong understanding of compilers to program anything complicated. These days you can use a high-level programming language and never get down to the level of the compiler if you don't want to.
If someone wants to make lots of money or change the world with AI, my advice would not necessarily be to start with a PhD. It would be to focus on understanding data, getting very good with a library, and building apps that are useful to people.
If you do that, then getting additional knowledge about the mathematics furthers your career, but your career doesn't block on acquiring that knowledge.
If you do this, you probably won't have a great of chance of working on a team at Google or Facebook improving the implementation of the AI infrastructure. Just as you probably wouldn't get a job at one of these companies optimizing the compiler if you didn't have an academic background or years of experience in compilers. But you could still work on other teams in those companies and make as much or more than those people and have a more direct impact than just making it marginally faster.
I have a PhD in pure mathematics, and I don't do ML. Getting a PhD is a particular journey, and it's not for everyone. Also, the idea of getting a PhD as a credential for industry seems a little odd to me, but that may be my personal bias.