Your point is definitely valid. If housing costs double and salary doubles, you will have more income for things that don't change price like shirts and laptops in the high-cost area.
However, one of the things you lose in high-cost areas is freedom. You lose the freedom to pursue passions, take time off from work, try out a job you think you might love but pays 30% less, etc. I can delay or forego the purchase of a new shirt or laptop to prioritize something else in my life. Maybe I want to work for a non-profit I find compelling or spend time with my children. The high-cost area isn't high-cost for discretionary spending. It's high cost for essential spending.
If I need $75,000/year on housing, I can't afford a pay cut; I can't afford part-time job and part-time parenting; I can't afford passion. $75,000/year might sound like a lot, but the median home in San Francisco is going for $1.35M. After a 20% down payment, mortgage payments would likely be around $65,000/year. Add on another $10k for taxes and we're at $75,000 for a median home.
Let's say I could earn $250,000/year in San Francisco and $100,000/year in Chicago. In Chicago, the median home is $300,000 so we're talking $15,000/year in mortgage payments instead of $65,000. Let's assume that I pay 30% of income in tax on $250,000 and I take home $175,000. After $65,000 in mortgage payments, I'm left with $110,000. In Chicago, If I pay 25% in tax and $15,000 in housing payments, I'm left with $60,000. That's certainly less, but I've also gained a lot of freedom. If I want to take time off, my expenses are low. If I want to switch to a career earning $50,000/year, I can still live my life. I'm not being forced into specific employment based on cost of living.
If we adjust the numbers slightly and make SF $200,000 and leave Chicago at $100,000, the gap quickly closes. Assuming 28% tax on the lower income, we're talking $79,000 vs $60,000. A little more disposable income, but very little freedom.
SF salaries are certainly high. Are they 2.5x higher? Even if they are 2.5x higher, do you really feel good? I guess a part of me feels like life should be easier and more comfortable. I'm not looking for fancy shirts and yearly expensive laptops. I'm looking for the comfort of knowing that if something goes medically wrong, my cost of living isn't so high that I'm very quickly on the bubble. I'm looking for the ability to be able to choose different life priorities in my future if I desire. We all make our own decisions, but I think there's something intangible that lower cost of living provides.