In some aspects, kanji work like the letters of the (Roman) alphabet.
If you were to teach English to a student, you could say that the basic pronunciation of the letter “s” is a hissing sound. That’s what WaniKani does when teaching the kanji reading.
Later on, you begin teaching actual words, and point out to the student that “s” is pronounced differently in “say” (hissing sound) and “dogs” (buzzing sound), just to give two examples. That’s what WaniKani does when teaching vocabulary with different readings of the same kanji.
This happens all the time! Think about the letter “a” in “cat”, “car”, “paper”; or the letter “i” in “I” and “is”. Now imagine that, during the English alphabet lesson, you try to explain to your student the specific intonation of each and every one of those “a” and “i” pronunciations, not as parts of words, but as independent sounds. That would be much harder to explain, and would probably overwhelm a beginner student! It makes much more sense for the student to learn all of those different pronunciations of each letter over time, as part of the pronunciation of entire words.