Sure but if you are accidentally jailing an innocent person it's quite likely that out of all people you could convict you had the most evidence for convicting that person. I don't think the model that lets more guilty people go free in order to avoid convicting the innocent is somehow able to convict the second or third most likely suspect for this crime when that's the person who's actually guilty.
I don't think it's a false dichotomy. I think roughly speaking you calibrate the standard of evidence for a conviction and a good approximation to how that is calibrated is the ratio of guilty man set free to innocent men jailed. This is calibrating the ratio of false negatives to false positives. To avoid false positives you want fewer convictions which is generally going to result in more false negatives. Yes every time you get a false positive, you also have a guilty person go free, but chances are that person was always going free, since they were never the most likely suspect and were unlikely to ever be tried in court.
I don't think it's a false dichotomy. I think roughly speaking you calibrate the standard of evidence for a conviction and a good approximation to how that is calibrated is the ratio of guilty man set free to innocent men jailed. This is calibrating the ratio of false negatives to false positives. To avoid false positives you want fewer convictions which is generally going to result in more false negatives. Yes every time you get a false positive, you also have a guilty person go free, but chances are that person was always going free, since they were never the most likely suspect and were unlikely to ever be tried in court.