Phonetic alphabets have strong precedents - and have had strong backers - in English as well. See the Shavian alphabet[1] for a relatively recent example. Others were drawn up by such as Benjamin Franklin and Sir Isaac Pitman, famed for his shorthand.
One of the greatest impediments to these systems was that, while pronunciation may be picked up from spelling in a so-called phonemic system (assuming a bog-standard means of determining stress, which English doesn't have), spelling does not always follow from pronunciation - not unless you happen to speak precisely the English that the standards body prefers. English phonology, particularly when it comes to vowels, varies so wildly from place to place that any new, purportedly simpler system will be met with resistance from the majority of speakers to whom the system seems to be wrong, messy, and arbitrary. As a simple and common example, that of 'Mary, merry, and marry': do you collapse these three vowels, as many English speakers do, thus frustrating those who would like to make the distinction in print; or do you retain the three and in doing so create three new arbitrary-seeming spellings for words that to many speakers are homophones? Do you, as in Shavian, retain an R at the ends of "star" and "mother," or do you bow to common British pronunciations and excise these in spelling as in speech - something another phonetician, Henry Sweet[2], would have recommended?
(We see something similar in the promotion of and resistance to new programming languages: fixing some problems is not always enough to attract adopters away from a language which is at least doing the job. Imperfections stand out in novel tools, even if other improvements have been made and the imperfections are nothing new.)
Shorthand authors were well aware of the difficulties in teaching a "phonography," or phoneme-based system, to a duplicitous student body. This is one of the reasons that many English shorthand systems do away with almost all vowels, except perhaps to indicate where the vowel occurs and what broad family of like sounds it belongs to. Of course, eliminating vowels is one of the best ways to promote speed in writing; but there was also the problem that, where writing a vowel was desired (e.g. to differentiate 'tarp' from 'trap'), not all students will agree on which symbol ought to be used for each vowel sound - the sound varying from person to person, even within the same county or town. These shorthand systems were left ambiguous on purpose, so that teaching speed might be improved alongside writing speed. No need for a student to learn whether the first vowel in 'father' is indeed the same as the one in 'bought' - and from whose mouth, anyway?
It is possible that in an IPA-based system, English spelling may differ from person to person as widely as pronunciation does. Surely, however, that would make things more difficult for second-language learners than having to contend with one standard that happens to be riddled with inconsistencies? (Or perhaps not?)
[1] https://en.wikipedia.org/wiki/Shavian_alphabet
[2] https://en.wikipedia.org/wiki/Henry_Sweet