The rules for pronunciation is very directly linked to the spelling, with few exceptions.
Sure, as long as you assume the only goal is to validate a phonics approach to teaching reading. Some people appreciate that english words get the same spelling in Minnesota as they do in Mississippi.
For foreigners like me that mostly use it in text, the biggest overhead is in speaking, for example I always mess up the words study and student, it's infuriating.
Even if there are dialects that pronounce the same word differently, you could still find a lot of common ground.
If your biggest problem lies in a circumstance you rarely encounter, arguably fixing it is not a priority.
> for example I always mess up the words study and student, it's infuriating
This is a funny example to use, since it fully conforms to the rules I described above -- study uses the STRUT vowel, and student uses the GOOSE vowel. It would be a better example for the complaint that we have more sounds than symbols.
It's like a config file specification that supports gotos.
It's like in English, if you say "y'all" and write "ladies and gentlemen", you understand that those might mean roughly the same thing but are different words. It's not a spelling issue.
This is an important but hard to articulate distinction. Ask more if it's unclear...
What you really want, for learning to read and write via phonics, is determinism -- you want someone to be able to write something if they know how it sounds, and to be able to read something if they see its written form. There's no need to have symbols and phonemes correspond one-to-one, and they generally don't even when people are devising their own orthography in a green field.
For example, using C for a generic consonant, we have the following regular spelling rules in English:
Voila, ten sounds in five symbols. The problem from a phonics perspective isn't that we don't have ten different vowel symbols for these, it's that we have other ways of writing the same vowels ("beat" is not written "bete") and other ways of reading words that appear to conform to these rules ("debris" does not rhyme with "priss", or even with "his").