Yep. That's why when I FIREd I moved. In the past 10 years I've either lived in 2 of the very brightest blue states on that map (Hawaii and Maryland) or I lived in Tokyo, which if it was on the map, would be even brighter blue than anything in the US. I moved to Georgia, which is one of the lower cost of living states. Not THE lowest, but still quite low.
I am not exaggerating for Tokyo. I paid about $50 for electricity last month here in Atlanta. In Tokyo, it would be about $150. For the same kwh usage. And this is fall, where I don't run A/C or heat. It was worse in the summer/winter.
It's worth staying in HCOL areas if the pay you get from your job makes it worth it. But don't stay in that HCOL area once you retire, unless you plan to take longer to build up your $$ stash for the luxury of that.