The specialty card would drastically change. I wouldn't even know how they'd accept students. Currently, students with scores in the mid/high 90's would apply, while students with lower scores'd be discouraged and not apply. Now there'll be a surge of applications to the specialties, because those students that normally wouldn't have made the NBDE score cut would now apply. There'll be a flood of wouldn't-have-applied students applying and there's no standardized screening system.
I don't see how specialty programs would create a new test, as there's not yet a central agency to write, distribute, and test questions. The ADA did all that for the NBDE, but specialty departments simply do not have the resources to develop a new test AND test it out with current students.
Residency programs still want top students, and they have to work with what they have remaining. The DAT score can still serve as an admissions criteria. Class rankings will probably become more important for many schools. The problem, however, is in the unranked schools. There are only a few select schools can pull off the no-rankings system, because they're the top schools. But how would a program distinguish the top half from bottom half of Columbia? If a lower tier school were to try to not rank, then the specialty programs would be severely turned off because they can't determine who the top 5% of the class are, and they may not risk accepting students. The reputation of the school is one of the biggest remaining indicators of student quality. It matters now more than ever. I really wished I had known this, because it would have played a part in deciding which school I attend. It would be to everyone's advantage to attend Harvard, Columbia, UCLA and to a moderately lesser extent Penn and UCSF if they were given a chance.