While I'm not liking your phrase "bad regional accents" I do think you have a point. There are many, many different English accents and to attempt to capture that in the orthography is too much hassle and detail. The "dictionary pronunciation" is really more of a proto pronunciation than actual dialect-ized speech. It is a generalization and standardization and to an extent "the correct" way to say something Which is prescriptive, ugly and discriminatory and quite likely also racist. But there really is a need to simplify and standardize instead of capturing every tiny nuance of all dialects.
In my mind the best way to do this is just pick what you believe to be the most standard English accent and use that. Acknowledge that there are countless dialects. But this is the standard.
Mon Dieu!!! Zut alors!!! Quelle merde!!!