Wouldn't that deter prosecutors from going after relatively minor crimes that are less likely to lead to a conviction?

Not really, a plea bargain resulting in any punishment at all counts as a conviction for the prosecutor. A case like CP or cocaine possession which are in most jurisdictions basically straight liability crimes are very nearly guaranteed convictions. Plus, it never looks bad for a prosecutor to have convicted a child pornographer when it comes time to run for re-election. And not prosecuting such a case would lead to ads run against you saying that you're soft on child rapists.