I think a mixed system is fine. As long as robust public systems exist, I also am fine with private being there. I might go private myself if it meant I could get faster appointments and a doctor I could understand. My GP is booking 2 months in advance these days, and my only alternatives are doctors with such heavy foreign accents I can barely understand them. It’s only going to get worse with mass immigration.
That’s kind of the point. We live in a system that is supposed to be “innocent until proven guilty”. Not because people who commit crimes should get away with them, but because the opposite system would be completely untenable. How exactly is he supposed to prove that he is innocent? I don’t care how sure anyone is that he did it. Prove it, or by our legal standard, he must be considered innocent.
If you want to live in a society where accusation is tantamount to fact, you’re going to regret it as soon as anyone says anything about you.