I currently work for a US tech company here in Tokyo, but previously worked at a local tech company.
I've lived in 3 separate places in Tokyo (and currently own an apartment), and everything I've lived in has been bigger and cheaper than my apartment in San Francisco. I currently live in Sangenjaya (central Tokyo, a couple stops from Shibuya) and my mortgage, insurance, HOA, and total expenses are cheaper than my rent alone in SF.
My income is lower, but not in a way that I actually feel, because the overall cost of living is considerably lower in Tokyo. The conversion rate only really matters if you're going out of the country. There's been barely any inflation, so if anything, as the rate eventually goes back to normal, things will still be considerably cheaper here.
Yes, a lot of people live in tiny apartments here, but the cost of those units can be really cheap. You can pay ~$400 a month for a tiny unit here, which you simply can't get in NYC.