We had a semi-interesting discussion in class about 読み方 (yomikata) – which is to say, readings of kanji. When you see a character, there are often multiple ways it can be pronounced: 人 might be hito, jin or nin, and in some compounds hito becomes bito, in the same way that handbag isn’t pronounced like a combination of hand and bag, but as hambag.
We ran into confusion with 日, “day” or “sun”. This has yomikata of hi, bi, ka, jitsu and nichi. Except that this is clearly not the end of the matter, because in the very common word 明日, “tomorrow” none of those sounds appear. The word’s pronunciation is, in fact, either ashita or asu (myounichi exists, but is very formal).
This caused a minor argument-slash-misunderstanding, because I suggested that one yomikata for 日 is ta. The teacher disagreed, on the basis that the whole word is pronounced as ashita, but that doesn’t mean anything for the individual kanji. I don’t pretend to have any authority to argue with the teacher about whether this is officially true, but I do think it’s confusing.
I suppose this comes down to ways of thinking. I don’t know what the ‘point’ of yomikata is, or whether anyone has actually defined it. I assumed they were a system for classifying the possible pronunciations of kanji, and under such a model omitting ta* would be a failing: a person encountering the word 明日 for the first time would be totally unable to come up with the correct pronunciation, despite having a perfect knowledge of all yomikata. This is presumably not the only word which has a pronunciation not reflected in any yomikata, either.
* shita is probably better on reflection because 明 does have an official yomikata of a
So basically, I think if you think of yomikata as the set of official kun-yomi (Japanese-devised) and on-yomi (Chinese-derived) readings for kanji, then indeed shita does not exist, not being on the list. However, if you think of yomikata as the real-life set of possible ways to read a character (as its name would suggest) then one of the ways you pronounce日is, indeed, shita, in the word 明日 if nowhere else. It’s all a bit confusing! The omission seems arbitrary (I don’t know whether it is arbitrary, and it doesn’t especially matter).
English has a related problem, in that pronunciation is really only defined at the level of the word, though there are of course many patterns that exist between similar words and are reflected in spelling, so a lot of extrapolation is possible. I suppose the difference is that a) I’m a native speaker, b) our alphabetic writing system works quite differently from syllable-based kanji, and c) as far as I know, there isn’t an official list of possible pronunciations for English letter combinations claiming to be complete and authoritative.
I would tend to argue that, for a person learning how to pronounce kanji (so, anyone who ever learns Japanese, including Japanese people), it's more useful to include all possible pronunciations of a character rather than just a subset. You can of course learn idiosyncratic words like 明日 entirely separately, but I generally think having a comprehensive mental model is more useful than a partial model and a string of special cases. However, I am not World Yomikata Authority so it doesn't really matter what I think.
The short version is, I suppose, that what yomikata exist for a word depends very much on what you think yomikata are, and the official answer is, official yomikata. Be aware.