Even if you have good Bayeianisms, you might still want to throw out prejudicial information that isn't likely to be relevant. It is safer that way and doesn't rely on making as narrow an estimate about how good people are at being rational.

Alternatively, it might make sense to do away with juries altogether and simply have judges decide everything. However, there's some evidence that judges are not much better than juries at deciding cases. So I'm not sure that would help much.