OK lets say we implement this approach, we know there will be some people who will be wrongly executed because they were wrongly convicted. (We know this because we know justice systems are not perfect because we have plenty of evidence to show they aren't.)
Are you willing to take your chances of not being one of those wrongly executed?
And is there a sort of cut-off line at which you would no longer consider your execution policy workable? For instance if it was say 1 out of ten that was wrongfully executed or 1 out of 5 or any other figure?
The other point, of course, is that the violent felon would have absolutely no disincentive to kill the victim if he or she was going to be executed in any case.