I have a lot of criticism for the U.S. criminal justice system, but I've also got first-hand experience with it and I think your assertion is inaccurate. As a judge's clerk I saw the files of numerous criminal convictions on appeal. I can't think of a single one where there wasn't overwhelming evidence to support the conviction.
The felon caught with a gun in his car, or the drug dealer who tried to sell drugs to an undercover cop, or the guy who was arrested after beating his wife bloody. That's the bread and butter of the justice system. You can argue that two of those three things shouldn't be crimes (and I agree--but at least half the country doesn't) but the idea that people are routinely convicted without evidence is a myth.