I don't understand, does Japan use a scheme to romanize words that is based-ish on a version of English that is long dead? That seems like a lose lose for everyone.

Japanese vowels are simple and consistent, for example 'e' is always the 'e' sound in 'bed', but (due to the history of the English language) English speakers are used to taking in the context of the vowels and pronouncing them in a variety of ways. When reading Japanese (in which the surrounding letters do not provide any hints as to how to pronounce the vowels), English speakers often end up guessing at random, sometimes pronouncing 'a' like in 'cat', sometimes pronouncing it like in 'father', etc.

Since Japanese has simple and consistent rules for vowel pronunciation, and Japanese people aren't used to hearing much deviation from these rules, this often means what the English speaker is saying is entirely incomprehensible to them.

There's simply no reasonable way to base a transcription of another writing system on English phonology because the latter is highly irregular. It would also confuse literally anyone else who uses Latin script.

English speakers who want to pronounce words in any other language correctly will probably just have to get used to the fact that they need to unlearn some habits.

A transliteration or transcription scheme that uses <ch> for [tʃ] and similar sounds and <j> for [dʒ] is obviously influenced by English habits, yes. Doesn't mean the same scheme can not use <u> for [u]...[ɯ] and <e> for [ɛ], though.

Nobody suggested to write 'Fookoosheema', but maybe someone should... no?