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I actually have recent experience of living with a fuel heater in central Tokyo (Yoyogi). My husband’s grandmother didn’t like Air Conditioning and never used it, so in the winter months the sources of heat were hot water bottles (for the bed), the heated toilet seat, the kotatsu and the fuel burner. Like many Japanese people I grew very fond of the fuel burner.
To understand this perhaps you have to think of it as a progression of the irori (the fire pit that used to be the hearth of the home, now only used in very few houses). The fuel burner is a complementary source of heat to the kotatsu - one sits at the kotatsu with a kettle on top of the heater and access to hot tea throughout the day. My grandmother-in-law would also prepare foods on hers (like hot mochi or yaki-onigiri or toasted dried squid).
I only got a few winters with this arrangement but I treasure them and am not at all surprised that the tradition continues.
My grandmother-in-law’s son lives in Zama in Kanagawa in a relatively modern apartment block. He and his wife are a bit, let’s say “alternative” - part of a Buddhist/Christian sect that values organic foods and natural medicines (hard to explain quickly) but they don’t like A/C or central heating either (quite a lot of people in Japan believe it makes you ill more - and not just in Japan) so they too use the fuel burners.
Not my father-in-law. Centre of Tokyo (Minami Azabu), smart, recently refurbished/rebuilt apartment (something commonly done every 30 years or so) and he uses the A/C to heat the house in the winter. I do spot burners from time to time in some of the older houses in his area, I also know that some of the neighbours in his apartment complex use them. I believe it’s the kettle heating capacity as well as being a source of warmth that helps their existence persist so.
Unless the winters in the flatter parts of Honshu, Japan become harsher and longer, I don’t see fuel burners being relegated to history in my lifetime.
But yes, straight from the bath (with your skin red and glowing) and into bed is the traditional way to spend the end of the evening. There is nostalgia for this, believe it or not (brings some peace to tired parents! Those kids aren’t going anywhere!!!)