It's also a little misleading to compare the numbers that way. It usually takes a lot longer to become a psychiatrist in the first place. Your cumulative earnings in the first ten years after graduating high school might be higher as a plumber; in fact, I suspect most people who become doctors actually lose net worth throughout those ten years due to student loans. They just don't count towards the median income for a psychiatrist because they spend much more time not being a psychiatrist.
Once the plumber and psychiatrist are both in a position where they're running their own business or practice, their income is more of a conscious choice than it is for someone who's working for an employer. Self-employed people can and do sometimes choose to earn less money in exchange for more free time, and it's a lot easier to do that when you don't have six figures of debt at the start of your career.