Lyman Stone has a good blog post[1] suggesting that it's rational for Millenials loaded down with student loan debt to live in high cost-of-living regions, for exactly this reason. The high nominal incomes give them more power to repay their student debt, which is not cost-of-living adjusted.
This worked for me. I borrowed way too much money going to school. As a fresh MBA grad in the suburbs of Los Angeles, California, with few marketable skills, I couldn't find any career options that would offer a starting salary that came close to covering my costs.
My big break was finding a job in San Francisco. I charmed my way into an entry level sales gig with a base salary of about 35K USD (in 2004), and was soon making at a 70K-ish "annual run rate" (stealing that from startup PR lingo). And that job did all of the lead generation for me. I wasn't able to find a job like that outside of a big city.
Even when I was homeless for a bit a few years later, I chose to stay in San Francisco over moving in with my suburban LA parents because there I saw more opportunity in San Francisco. For me, it was riskier to play it safe in the burbs than hustling in San Francisco. It's better to burn out than fade away.
The way I see it, if you wanna make it as a professional, and you don't have a reasonably understood career path to follow, it makes sense to go where the money is. You can live financially cheaply in most places, and you'll have to decide how much you're willing to work for it. For me, living in San Francisco is, and has been, worth it.
[1] https://medium.com/migration-issues/millennials-have-less-de...