Japanese has 3 forms of writing (not counting use of the Latin alphabet and Arabic numerals). 2 of them are used to write phonetically, and each has about 50 characters. They aren't too hard to learn, and are the closest equivalent to "letters" in written Japanese. One is used for phonetically writing Japanese words and for grammatical particles, and the other is mostly used for foreign words, sound effects, or things that you want to bring special attention to for some reason (I've been told to consider it similar to writing something in italics, maybe). The shapes of these have a somewhat-distant etymology to Chinese characters.
Beyond that, there are 10s of thousands of characters with a much closer correspondence to the Chinese ones (although perhaps a number in the low thousands are commonly used in everyday life). About the first thousand are taught to grade schoolers. I don't think that the correspondence is perfect, but these are supposed to be the more common characters, in general (and are taught earlier for that reason). Roughly the next 1000 are taught during middle and high school.
As a Japanese learner, we tended to have example sentences that introduced new grammar constructs, new words, and new characters for those words (if they're commonly written non-phonetically). I think by the 4th semester of class, the goal was to have mastery of the ~100 phonetic characters (the hiragana and the katakana), along with perhaps 500 of the non-phonetic characters (the kanji), along with different ways that various characters would be pronounced when used in different words.
In general, I feel like we did cover legitimately useful words and characters, but that if the text (literally) left out the less-used "letters", it'd be a premature optimization that wouldn't gain you much. If you mean that more commonly-used words should be given priority, then I agree, in principle.