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.
> Japanese primary and secondary school students are required to learn 2,136 jōyō kanji as of 2010.[4] The total number of kanji is well over 50,000, though this includes tens of thousands of characters only present in historical writings and never used in modern Japanese.
They might have passed some level of the kanken (kanji kentei) in school but it is unlikely to be level 1. The gap between level 1 and 2 is ridiculous.
A typical font contains around 7,000 characters. In everyday use, you rarely touch all of them—most situations stay comfortably within the realm of jōyō kanji. However, there are many edge cases, especially with personal names, where the required characters fall outside the jōyō set. Fonts must be prepared to handle all of these possibilities, including the less common name kanji.
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.