I'm guessing this is prevalent in Japan not because "all the good domains are taken" but because (browser) support for unicode domain names (IDN) continues to be patchy, especially on mobile browsers which, as far as I can tell, are especially popular in Japan. I'm guessing they've long solved the problem of entering Japanese characters with a tiny keypad for things like text messaging, and I strongly suspect that entering names in their native script is much nicer than entering transliterated or foreign names.

Besides, punycode isn't especially efficient. I suspect you quickly run into the DNS hostname length limit as well, as the number of punycode characters required increases with the numerical value of the code points to encode. I'm too lazy right now to work out how many Japanese characters you can maximally encode in a domain name. :)

Note: I don't speak Japan, have never been to Japan and am generally out of touch with Japanese culture. My first language (German) only uses a small number of non-ASCII characters, so I'm not exactly an expert on IDNs.