The perfect English abjad would use diacritics to mark vowels and some clever way to identify syllable boundaries (so you can distinguish ideal from idyll). But alas, we’re probably stuck with an alphabetic script forever.
This one took a moment. (It's "naturally", not "neutrally" or "entirely".)
The rest is surprisingly readable.
"Thee proplem weth a systhemateck, fhoneteck chaigne en
Englush speleeng es thet et raeses thee questeon uv wut
aksent to faivor. Fer an Americon en Oheo, thees
transkriptshon probubly maeks sum sens, wunce yu get paest
thee skwaw. I daut an Engleshman or eaven a Nue Yorcer wud
fynd et ueseful."
please rewrite it but this time with a Southern drawl "Th' proplem weth a systh'mateck, fhoneteck chaigne en
Aynglsh speln iz thayt et raeses th' questyun uv wut aksent
ta fayver. Fer a Amur'can down yonder in Ohayo, thees
transkripshun prahbly maeks sum sens, wunce y'all git past
th' skwaw. Ah daut an Engleshman or ev'n a Nue Yorcer wud
fynd et much ueseful."
- GPT-4 / https://sharegpt.com/c/Q5DW1wgAnd it doesn't solve the problem on the graphematic level. It ought to allow anyone to read the chosen dialect phonetically. But it suffers from an arbitrary choice of glyphs, so I have no idea how to pronounce eg. an (an actual problem I have pondered today is a-typical).
Conversely, if the spelling ought to be predictable for language learners, you are probably better of learning Mandarin (^_^)