For starters, there is a time where foreigners learning a foreign language must leave their script behind and use the actual script of the language in question.
Which, imho, is the time they decide to learn the language.
However, from the way you're speaking, you must not be a fun of Romanization.
Romanized Japanese have their place and purpose. But it's not how Japanese people write their language, at least not yet. Substitute Japanese with Greek or any language that's not written in some version of the latin alphabet.
English is not the only foreign language taught in Japan, and it is a common practice to use Katakana equivalents to teach how to say things. It's only natural.
I've seen textbooks Furigana everywhere
This is probably why EngRish persists. Japanese language and therefore katakana do not distinguish /æ ʌ a ɑ ə ɜ/ using ア(ー), thats 6 common phonemes in English though (same in Greek, half of them merge to <α> and the rest to <ε>. My first English classes used transliteration is the Greek alphabet as an aid, and in combination with teachers not caring to correct students' accents, explains why most Greeks and Cypriots suck at spoken English, like me)
. Katakana as it is used now, no way it can help them. And if you invent a bunch of new combinations to represent sounds that are not in Japanese, I don't think it will be easier for them than learning the target spelling in the first place, imo.
It's even more common to show readings for Hanzi and Hangeul.
Chinese and Korean have a ton of consonants that are allophonic in Japanese (for example シ can be xi si or shi in Mandarin).
Such pronunciations are OK if you are borrowing a new Chinese or Korean word in Japanese, but not if you are learning to speak the language. That's way Japanese sound funny to Chinese and Korean speakers as you said, isn't it?
Oh, and as for IPA in respect to English, that is almost if not completely futile. You can go down any given street in America and get a different set of linguistic data from individuals. It's why there is spelling to give an approximation. lol
Of course there will be allophony. Educational IPA is broad transcription. What you need is a way to show that, eg luck
have the vowel, whether it is [ʌ], [ɐ] or [ʊ] or something else. IPA can do it, phonetic respelling can do it. Katakana cannot do it. It merges more sounds than it should.