Speaking of which, it seems that the only case of spelling adapting to pronunciation in English is the commonly used spelling "me" for "my" in Irish dialects.
'h饜懍se' and 'aut' - where 饜懍 is read as 'au' in RP, but as 'oy' in NI.
The downside is that the said alphabet would have more letters and it won't be always easy to guess the spelling based on pronunciation (still easier than currently in English), but the upside is that one can always read any word correctly in their accent.
here is an interesting article listing digraphs in various languages with latin script that have lots of examples where the same sounds have a single letter in other languages:
I really want to hear a New Zealander quote "The pen is mightier than the sword".