The bar is an imperfect filter. One could study for the exam and pass and still be hugely deficient in ability as an attorney.
I would argue there's no exam that could replace the evaluative and experiential component of 3 years in law school, and accreditation helps enforce at least some standard of quality in the profession. More incompetent lawyers -> more wasteful behavior -> a more bloated and slower legal system -> worse outcomes for everyone.
I think reducing barriers to completing the legal education (part-time programs, lower cost, etc) are better avenues for increasing access.