Appeals courts don't deal with the specific facts of a case, I believe, but concern themselves with whether the process carried out was consistent with conviction beyond a reasonable doubt. The appeals court isn't going to wait until some new evidence is created by the prosecution.
If the appeals court sets aside the conviction because of false evidence presented by the prosecution, then the situation reverts to that which existed prior to the conviction; that is, that the accused has the right to bail.
I would predict a great number of cases will simply be dismissed with the prosecution having to settle for time served. At some point the appeals court would have to decide that the prosecution has run out of time to provide a speedy trial. Cases which might be reasonable to pursue within a year of the crime might become very difficult to prosecute, say, three years after the crime. Witnesses die, disappear, retire, and may just become forgetful.
Good point, thanks.