When I select 'Japanese' on fonts.google.com the number of fonts drops from 1901 families down to 50. Selecting 'Hiragana and Katakana' raises the number to 81.
That's still a lot of fonts, but it's not 2000. I guess designing a font for a language with 2100 different characters is probably a hassle.
I suppose you're counting the joyo kanji plus kana alphabets with diacritics. But the actual count of kanji is much higher, even if Japanese uses a relatively small number of characters for day-to-day writing.
Pretty much every native university student I met when I studied there, had passed the Kanji Kentei level 1 test. A certification of proficiency in around 6000 kanji.