I know each word has its own correct kana spelling. But they are all pronounced identically as “ō”, right? So if you don’t know how to spell a particular kanji reading in kana but you know how to pronounce it, why does wanikani treat it as not knowing the reading?
This is a genuine question about the Japanese language, as I still just can’t wrap my head around why it’s important 
It’s etymological!
In 1946, they re-did all of the official kana spellings so that the way things were spelt actually reflected how they were pronounced. Readings like ～おふ, ～あう, ～をふ, ～わう, et cetera et cetera, became ～おう. Readings like ～おほ and ～おを became ～おお.
～おー is generally reserved for katakana, though.
Why’s it important? Because that’s how they’re spelt. 
That said, the vast majority of long-o sounds are ～おう. There’s literally only about a double-handful of words that use ～おお.
This is the part that I don’t understand.
I thought お父さん was spelt お父さん.
Why isn’t it enough? If you know how to spell a word and you know how to pronounce it, then in what life situation would you need to know the correct kana for it?
I’m sorry if this is a silly question, it’s just such a new concept to me
When you’re trying to type it on a keyboard. 
Some IME auto-corrects might recognise おとーさん as an attempt to type お父さん, but it’s not really safe to rely on auto-correct to fill in the gap for you.
Is this the only reason? I’m sure there’s something I’m missing, because if this had been the only reason, then keyboard creators could have surely made the keyboards more permissive by suggesting 父 no matter which combination you typed…
Unfortunately, this is one of those things that ultimately just comes down to “it is how it is”. You can try petitioning the Japanese government to make all the spellings consistent (get them to deal with the づ／ぢ issue while you’re at it), but since it hasn’t even been eighty years since the last reform, they might be a little resistant to the idea.
Why is knight spelled knight and not night? And while we’re at it, why not “nite”?
There’s something funny to me about a person writing in English complaining about another language having more than one way of expressing the same sound in writing^^;
Dearest creature in creation study English pronunciation etc (the poem has over 800 examples of irregular spellings in English, according to Wikipedia)
Whale oil beef hooked
Also, the one rule of English spelling:
(not my joke)
I love this poem!!!
But it’s different, isn’t it? In English it’s enough to learn one spelling for each word.
There’s only one spelling for お父さん too
In Japanese there is one (kana) spelling for each word, plus the kanji version for words that have one. I thought you were asking about why there were different ways of expressing the same sound using kana?
I don’t think that’s quite right, since certain words (EG: 明日 and 塩味) can actually be spelled / pronounced multiple ways (あした, あす, みょうにち for 明日, and しおみ and しおあじ for 塩味).
There might be some nuance added based on the specific word and which version of it you use, but you get the point. Though rare, there are cases where the same word can have multiple correct kana compositions.
I think its as simple as oo and ou are not the same, there is a slight sound difference and while a lot of people dont know at the start of their Japanese journey, but there is a slight tonal aspect to Japanese. oo is flat and ou has a change. If you use the 10Ten browser extension and hover over kanji, you can see the change where the u is:
This would be different if it was o / -
Also above you mention that in english you learn one spelling for a word, I guess while true, there are variations like English and American English - Colour and Color.
I don’t think those examples count as “the same word.” They are synonyms that can be expressed with the same kanji.
It has the same root at the German knecht and in the past the k was not silent
I fart in your general direction you dappy English kernigit
Don’t forget children. They don’t go to school and know all kanji after grade one. It’s a long process to learn all the kanji. So children books are generally written in kana (katakana and hiragana) or with only a few kanji. And even after that, there are furigana - those kana next to a kanji to show its reading. That’s why there is a need for every word/kanji to also have a fixed spelling in kana.
If it has the same meaning and is written with the same kanji, I would definitely consider it the same word, but agree to disagree, I suppose.
