"Many people have been executed who later have been proved to be innocent." - "Many" is a strong word. The system mostly works. But if your point is that some have and that some is too many, then I'll agree. But no system is without flaws.
When the end result is death, I find those flaws less easy to casually dismiss.
A person convicted on moderately convincing evidence can always be compensated and released if better evidence (or advances in technological ability to interpret evidence) later shows the conviction was wrong
"Moderately convincing evidence"??

The standard in a criminal court is 'beyond a reasonable doubt'. If the evidence is only 'moderately convincing', the correct verdict is 'not guilty'.
The death penalty straddles the gulf in our legal system where we must, simultaneously, take it as being flawless and yet acknowledge its flaws. We can't treat a 'guilty' verdict as representing a certain
degree of guilty, case by case - they're guilty, or they're not. We have to assume when it comes to the sentencing phase that the 'guilty' is correct - the strength of the specific evidence that led to the verdict isn't relevant anymore.
And yet, we must also keep in the back of our minds that trial by jury isn't a flawless system, so in order to reflect that, we take our 'worst' punishment off the table
completely. That means that no-one is executed wrongly. OK, if you're in prison for 40 years and then exonerated, can we really 'pay back' the wrongs done to you? I doubt it. But we can at least
try. We can clear your name, we can try to make restitution. If you're 40 years dead and buried by our hand, tough shit. The punishment stands.