Not only that, it assumes that there is consistency and agreement among English speakers for those vowel sounds.
Not exactly. My spelling would be based on phonemics, not phonetics, so it doesn't need to account for every variant pronunciation. For example, this system would spell
Mary,
merry, and
marry differently—as
Meyree,
merree, and
maerree.
Of course, this spelling is based on a standard pronunciation, which is indeed not shared by all English speakers, but at least it's shared by a good number, as opposed to the five-hundred-years-out-of-date system that we use now.