And the magical accent corrector wouldn't fix bad grammar.
I'm reminded of a former flatmate whose father chose not to raise her as bilingual in the mistaken belief a second language would impair her learning. Instead, when she chose to learned Spanish as an adult anyway, she picked up the slang and pronunciation of her Colombian relatives, but never quite reached native fluency. She pointed out the drawback to having a local sounding accent and name instead of being an obvious foreigner was that everybody who met her assumed her misunderstandings, pauses or the odd really ungrammatical phrase was because she was an unusually stupid Colombian.
Aside from the obvious idea of masking one's visual identity for example through VR avatars in lieu of face-to-face interviews (to hide for example gender, physical appearances and able-bodieness), one's voice would still reveal many factors that could be used to purposefully or accidentally skew any neutral position one might have during interviews.
I know for a fact, that if I had the Indian accent to accompany my surname, I would be ranked lower or rejected altogether during interviews. I sadly have a slight rally Finnish accent, so even if my grammar were to be perfect, I'm not a good hire compared with native English speakers even if I'm just as capable for the same position.