This is a problem that other languages have already dealt with. Spelling doesn't have to represent the exact pronunciation of every word; it can represent phonemes, leaving some variation in pronunciation to dialect.

For example Vietnamese has considerable regional variation, some of which is reflected in the spelling system. The letter d represents /z/ in standard Northern Vietnamese but /j/ in standard Southern Vietnamese.

English already does something similar, as you've pointed out. In dialects that distinguish wh from w, the former can represent /hw/, whereas in most of England the distinction has disappeared and both are pronounced /w/. We don't need to respell whale because it already accommodates either pronunciation (although let's please get rid of "magic e" and spell it `wheil` to at least match the vowel).

Any linguist knows that a perfectly phonetic spelling system is not desirable. As well as what I've already discussed, pronunciation changes over time too. But I don't think that rules out spelling reform because currently English has many ways of spelling the same phoneme.