Why is the つく reading of 吐く not accepted–or at least not simply marked wrong? In other cases where readings are ambiguous, WaniKani tells you a different reading is expected. That’s not the case for 吐く, even though つ is taught as a 訓読み for 吐.
Is it because the reading つく is extraordinarily rare for 吐く, to the extent where you should basically always assume はく is meant instead? (Admittedly, I think I’ve only ever seen this sense of つく written in kana.)
Don’t know about the WaniKani reasoning, but unfortunately you can’t make this assumption. If you see を吐く, the reading is highly dependent on what comes before. If it’s ためいき, the 吐く is always read つく.
That said, I think it’s very often written in kana as つく to avoid any confusion or ambiguity, but not every author does this. I can check some books later today to see how often it happens.