Everyone knows why women withdraw their allegations.
Everyone thinks they know but, as far as I can see, no-one has ever bothered to ask the women concerned. So "everyone" may be right or they may be wrong.
But I note that you again turn to punishment and again suggest the death penalty, apparently with a higher threshold for proof than "beyond reasonable doubt". Whatever threshold you set, you would end up executing people for crimes they did not commit. We know from the USA, where the press can interview members of the jury, that juries misunderstand what DNA evidence does and doesn't prove, just as they misunderstand fingerprint evidence. I will never forget a case where a man was convicted of murder and condemned to death. The jurors, when interviewed, said that the deciding factor for them was that his fingerprints were found in the victim's home, where he was murdered, ignoring the fact that it was acknowledged by the prosecution that the defendant frequently visited the victim, so the fingerprints proved absolutely nothing. We have no reason to believe that juries here are any better.
The evidence is that the death penalty is not a deterrent. Some states in the USA have the death penalty, others do not. It is therefore possible to compare states that are demographically similar to see whether the death penalty is effective. If you do that, you will find that the murder rate is slightly higher in states that have the death penalty - not enough to be statistically significant and say that the death penalty results in an increase in murders, but enough to say that the death penalty is no deterrent. There is no reason to assume that rape would be any different, so you are proposing a solution that is unlikely to solve the problem.
What is a deterrent is the certainty of being caught, which brings us back to the real solution which is addressing the reasons why so many cases never get to court.