One would compare black defendants with guilty black defendants and white defendants with guilty white defendants. It's far from obvious that (guilty black defendants/black defendants) > (guilty white defendants/white defendants). Differing arrest rates, plea bargaining etc. would be factors.

60% of convicts who have been exonerated through DNA testing are black. Whereas blacks make up 40% of inmates convicted of violent crimes. Obviously this is affected by the fact that "crimes where DNA evidence is available" does not equal "violent crimes". But the proportion of inmates incarcerated for rape/sexual assault who are black is even smaller: ~33%. There are other confounding factors like which convicts received DNA testing for their crime. But it looks like a reasonable case can be made that the criminal justice system's false positive rate is higher for blacks than whites. Of course, the false negative rate could be higher too. If cross-racial eyewitness identification is to blame for wrongful convictions then uncertain cross-racial eyewitnesses might cause wrongful acquittals.

Yes. It's important to remember that guilty defendants aren't the same thing as convicted defendants. A rational decision-maker using Bayes' theorem wouldn't necessarily put all that much weight on the decisions of past juries, knowing as we do that they're not using Bayes' theorem at all. And, of course, a Bayesian would need exactly the same amount of evidence to convict a black defendant as they did a white defendant. That question is whether skin colour counts as evidence.

The conviction rate for black defendents is sometimes much higher than the conviction rate for whites, so the solution you've suggested here would intensify the racial disparity.