If you are not going to execute sexual predators, then the ONLY other solution is life imprisonment without the possibility of parole.
Surgical castration will likely never be allowed due to cruel and inhuman punishment grounds, and chemical castration can be and has been reversed by convicted sexual predators.
Besides the fact that you are ASSUMING that sex drive itself is the reason for sex crimes.
Given the current way the justice system works, with regards to appeals, you'd be hard pressed to actually execute or imprison for life an innocent person. Not saying it would not happen, just saying it would be unlikely.
Further, MOST juries require a higher burden of proof in cases where the two alternatives for punishment are execution and life imprisonment without the possibility of parole. Not to mention the fact that most appeals courts require not only a higher burden of proof (and use whatever means necessary to overturn a conviction they don't agree with), but also allow fewer, if any, reverseable/appealable errors to take place in such a trial without reversing it on appeal.