I don't believe our current system (in the US) is based on evidence, so I see no reason to limit alternatives to being backed by evidence. I've never had the opportunity to run my own justice system, so no, I can't say how well it works.
I think corporal punishment is vastly more humane and prefer it largely for humanitarian reasons. If we were torturing prisoners, and I proposed we stopped, would you ask for the evidence to back up the idea that cutting out torture was a good idea?
There needs to be some deterrent, but taking years from a person's life, and forcing them to live in squalid conditions and in close proximity to violent criminals, is not a humane deterrent, it is not an effective deterrent (as evidenced by recidivism rates), and it is not an effective deterrent in terms of either dollars or time.
Flogging, by contrast, can be executed quickly and cheaply, and, while the injury might stay with you for weeks, doesn't take a large quantity of your life. Flogging is also visually impressive and likely to be something that most people want to avoid. Flogging has a long history of use as a punishment too - suggesting it would have a useful deterrent effect.
Regarding execution - no mistakes can ever be corrected. If you send a person to prison and they commit suicide, die of disease, or are killed by another inmate, all of which are vastly more common in prison than in the general population, you can't undo your mistake should you discover that the person sentenced was wrongfully convicted. Likewise, even if you sentence someone for five years, discover after two it was a mistake, they do not get their life back. Does this mean we should never imprison people?
It's fine to say there should be a higher bar of proof required for execution, but the finality of the sentence is not a reason not to employ it. There are people who have committed heinous crimes caught on video, attested to by witnesses, placed at the scene by evidence, and who have confessed their own guilt, and who have no plausible defense. In such a scenario why should we stay punishment out of a paranoia that maybe, despite all evidence, we might be wrong and might one day want to release this horrible criminal back to the general population?