You might see 可也 in older books. Searching for it on aozora for example brings up lots of appearances in works of literature.
Generally I’ve found that whenever something is “usually written using kana alone” - that may be true in modern everyday contexts, but the kanji version can still very much be common in older works, kind of like how in English there’s plenty of words that would sound slightly stuffy nowadays but are common in old books and you still know what they mean. Conventions just changed over time to make it less common. The pick in the advanced book club right now uses a lot of kanji for words that I first learned in hiragana like that.
There’s also plenty of other contexts like proverbs, store names, and documents where the tendency to go with the hiragana might be lessened. So even in wholly modern contexts, I’m sure the kanji version isn’t nonexistent.
One other place you might see 也 is in names - I know of a 哲也, for example.
I’d probably associate it most with や in names at this point rather than 可也, so I could believe Wanikani included it mostly for that even though they don’t focus on teaching name readings.