If you insist on like-for-like, yes, so when I lived in NYC I just completely punted this question and didn't even try to live in anything like the kind of apartment I would have rented in basically any other city. I took a tiny, shitty studio in Hell's Kitchen for far less than I could afford and never worried about it.

Cost of living calculators assume you're trying to live in the same kind of housing in HCOL-city-A as you would have in LCOL-city-B, but there's no reason to accept this assumption.

I rationalized it this way: there is no amount of money in LCOL-city-B that could buy me the feeling of living in HCOL-city-A, so I'm going to treat the housing in HCOL-city-A the same way (i.e. mentally assume it's not available and consider that the tradeoff for getting the thing that isn't available in the lower-cost-of-living city).