I agree with the others; your mathematics to English analogy is quite off the mark. However, I wouldn’t go as far as to say that disregarding kanji readings is the same as not learning letters themselves.
Tell me, have you ever ridden a twocycle? Which do you like more, squares, circles, or threeangles? In a book, do you normally root for the maintagonist or the againstagonist?
Sure, the above questions may seem facetious, but in a language where you can spell out words to figure out how they’re said, these questions become much more serious. The way to type Japanese on a computer is to type out the reading, creating the hiragana, then locating the proper kanji that go with them. If you use only the kunyomi readings (as most early vocabulary on WK will teach you), you will likely never find any word you actually want once you start learning more jukugo (compound words).
Sure, in English, you can learn what “main character” and “opposing character” mean, but learning those will not help you understand when someone says “protagonist” or “antagonist.” English has letters we can use to figure out at least a ballpark of a reading, and we have WAY more vowel and consonant sounds than Japanese, meaning less likeliness of two readings being the same.
Here’s a very relevant, strong example most people would understand. Have you ever heard of the city of Higashimiyako? Probably not, right? That’s because it’s read Tokyo (or Toukyou by kana). If you only learn the vocabulary, than Tokyo (made with the characters for East and Capital) is Higashi, meaning East, and Miyako, meaning Capital. By learning the kanji readings (usually onyomi), you’ll understand how to acquire much more vocabulary without confusing natives.
Like @Leebo said, I can’t think of any kanji I’ve seen yet where the readings are used at all, but it’s true that WaniKani does have some less than practical instances of reading timings. One example would be 刀 learned at level 2. You learn the reading とう but then are given かたな for the vocabulary. You then don’t see the other reading for ten entire levels, around two months time at max speed, and that vocabulary is the ONLY one in the database to use the reading. It’s somewhat unfortunate when these rare instances happen, but it’s done for a reason. The radical is used in a lot of kanji, the vocabulary term is pretty much known universally in the English speaking world, and all of its jukugo use kanji that beginners shouldn’t be seeing.
If your argument is really about being against learning any reading but the one used standalone, I honestly think you may want to reconsider learning Japanese. If it’s related to the latter, then pick up some resources alongside WaniKani, as most of us do. If you want more vocabulary related to the readings, hit up jisho.org and search by the reading you want.
There’s another huge side benefit of learning all of the readings. As you get more kanji and vocabulary under your belt, you’ll get a “feel” of what the right reading is. Learning Japanese names is downright suffering, as there is a large list of readings that are pretty much used exclusively in names. When I encountered a person with the name 外山, I realized immediately that none of the readings I knew for it sounded correct when paired with やま, so rather than guessing, I asked how I read it and learned that と is a possible reading for it. If I’d learned only そと, I would’ve defaulted to そとやま and thoroughly embarrassed myself. Instead, I tried out がいやま、そとやま、and はずやま (I could have tried さん、but that is much less common in names), realized none of them worked well, and assumed their was another reading I didn’t know.
In English, the worst we can do to a word is either use the wrong vowel sound or put the stress on the wrong part of the word. In most cases of a native committing this error, we can immediately realize what they were trying to say. Japanese has a large amount of homophones, however, so it is much less likely they can figure out what you meant to say.