This is not about the Bar exam (the test), this is about accreditation of law degrees. The issue is about here is about who determines whether a legal education is sufficient to trust that a lawyer who passes the test is prepared for practice. This issue is the opposite of being completely test-based. The ABA also creates the most common bar exam (the MBE or multistate bar exam) but some states like California use a different exam. The legal profession does not, but many have long argued should, have a practice requirement for independent licensure to practice.

It is akin to ABET (previously Accreditation Board of Engineering and Technology) in engineering. having an ABET accredited engineering degree has long been a component (alongside testing and mentored practice) for being a licensed engineer who can stamp drawings (e.g., structural plans for buildings). There are two tests (FE and PE) but they are not created by ABET they are created by an organization called NCEES - The National Council of Examiners for Engineering and Surveying.

ABET and NCEES are different organizations, part of the confusion here is that ABA is both the accreditor and the tester in many states. The difference in path between accreditor -> testing -> licensure is:

ABA accredited degree -> ABA (MBE) or other (non-ABA) Bar exam -> Lawyer

ABET accredited degree -> FE exam (made by NCEES) -> mentored work experience -> PE exam (made by NCEES) -> Professional Engineer