Two thirds of the 133 Allopathic Schools in the United States, or Medical Schools, do not accept foreign students at all, and the rest, if they do accept them, are mostly filled by Canadian students. The Osteopathic Schools, which offer OD degrees and have slightly less stringent status requirements, have a slightly better chance for those who are undocumented at the time of application.
That said, about 1/3 of UCSD's 5,000 freshmen a year choose the school because of its highly ranked biomedical program, and most of them consider applying to medical school. But less than 20-25% of them are successful. So even with status, applying to med school is not easy. Your assumption that English shouldn't be a problem after four years is a bit of a leap of faith, and it may hold true for graduate schools that aren't medical schools, but the MCAT English test for medical school isn't just any language proficiency; the MCAT doesn't test grammar or vocabulary at all, but rather comprehension, thinking, and analytical skills. Asian students who excel in the sciences, even if they were born and raised in the U.S., will struggle with the MCAT English. For domestic students, the MCAT English is an even more difficult challenge to overcome.
So honestly the path that gives Chinese students the best chance of practicing medicine in the U.S. is the one you're already not considering. Graduating from a Chinese medical school, going through ECFMG, and passing the USMLE Steps 1~3, is a much more difficult path than applying to a U.S. medical school without residency, although the path is more difficult to navigate.