You're right, a system like that will codify some accent or other. Hopefully a teacher or school will use whatever dialect is actually spoken there.
If it's a transitional teaching alphabet, rather than a system to replace English spelling, that won't do any harm. The Fry list of 1,000 common words (available on unifon.org's Dictionaries page) has two pronunciations and two Unifon spellings for some words, starting with "the" (ħI or ħU).
(I'm faking some characters with ones out of "Character Map"; I apologize if they don't show up properly.)
The other problem is that Unifon doesn't seem to actually have a symbol for the 'o' vowel in "unicorn"; the 'o' in "ocean" is a diphthong, as in "o-u-shun". The intent seems to have been to make spellings similar to English spelling, rather than representing phonemes more or less one-to-one. The diphthong in "owl" could have been written "AŪ" as in "ant"+"ruler". (If I were a linguist I'd know some concise, precise terminology and notation for all this!)
They seem to overload the Λ symbol (as used in UNIKΛRN) for a couple of different vowels.
Skimming the Fry list, it uses O for "old", but Λ for other words with a similar vowel, and for a very different vowel:
old = OLD
door = DΛR
floor = FLΛR
story = STΛRI (but I'd write the final vowel I for "ee" as in "bee".)
more = MΛR
ball = BΛL
off = ΛF
office = ΛFUS
walk = WΛK
saw = SΛ
Apparently, English spelling looks so chaotic because spelling standardization (accelerated by the printing press) was happening at the same time as the Great Vowel Shift, resulting in "fossils" of Middle English that didn't change with the pronunciations.
... the vowel in the English word same was in Middle English pronounced [aː] (similar to modern psalm); the vowel in feet was [eː] (similar to modern fate); the vowel in wipe was [iː] (similar to modern weep); the vowel in boot was [oː] (similar to modern boat); and the vowel in mouse was [uː] (similar to modern moose).
(So maybe the diners that serve "chocolate mouse cake" made from chocolate mousse, complete with ears and whiskers, are on to something!...)
Much more at the OED's site:
One case of a random regional pronunciation in fact taking over is, as a matter of fact, the word "one":
Originally pronounced as it still is in only, and in dialectal good 'un, young 'un, etc.; the now-standard pronunciation "wun" began c.14c. in southwest and west England (Tyndale, a Gloucester man, spells it won in his Bible translation), and it began to be general 18c.
Somewhere I have a dead tree formatted book that makes the claim that almost all of the words in English actually follow a (rather complicated) rule set for spelling; you will oftentimes need to know what language we borrowed the word from.
"One" and "two" are among the fifty or so exceptions they listed.
Yes, it does drive me crazy. They don't spell out words or they use acronyms. Many I have to look up because I just don't know the meaning to all those acronyms. I've had people tell me that I am very formal because I spell out everything and don't use acronyms very often.
Does anyone know, or care, how acronyms differ from initialisms?
Do the formalists among us have a responsibility to know?
I don't usually care about being that precise, but...
Acronyms are pronounceable as single words, like "laser" or "scuba" or "NASA".
Initialisms are pronounced as separate letters, like "DVD" or "HTML" or "ATM".
(And some formalists among us can't stand the concealed redundancy of "HIV virus", or of entering a PIN number into the LCD display of an ATM machine.)
GC, I'm amazed, and I'm not kidding!
I've never seen so plain a difference between acronyms and initialisms.
Except that "NASA" (National Aeronautics and Space Administration?) satisfies both tests.
I've never heard people pronounce NASA "en-A-ess-A", only "nass-uh".
Some acronyms have lost their original capital letters. RADAR and LASER and SCUBA were the original forms for those acronyms, but they've become ordinary lowercase nouns. But NATO and AIDS are pronounced as words, rather than letters, yet they are likely to stay in allcaps.
"But NATO and AIDS are pronounced as words, rather than letters, yet they are likely to stay in allcaps."
Like so much else about human languages there might be little logic involved, but NATO and AIDS are initialisms, not acronyms, and for this reason might remain all caps.
I never heard of "initialism," and it's not in the lexicons of linguistic terminology that I checked.
Generally, if an acronym is readily pronounceable as a word (SCUBA, but not ATM), it will be. NATO and AIDS are acronyms (despite the other meanings of the phonetic sequence [eydz], which has been the subject of many a pun and comedic misunderstanding).
There is no way that I know of to predict which acronyms will remain uppercase.