Because it's mostly a stop gap even if you include the death penalty.

Its wild how little is actually done after these arrests. Sure they usually go to jail, but they are then also usually let out relatively quickly due to either low sentences (technically, non-violent crimes if they catch them ahead of time) or just the standard "overcrowding" excuse. And even in best case they leave after some years with little done to "rehabilitate" them, if not made worse because you have to go to jail to become a crook.

And then the sex offender registry and all of that sounds good on paper but very little is ever actually done to use that as a preventative measure.

Its similar a lot to the War on Drugs, where its used more as a political slogan to make those in charge look like they are doing something but the end result is about the same number of offenses because they are tackling it from the end point instead of trying to prevent the existence of the crime in the first place.

Deportations and community are important, as you said, but you also need to basically eliminate gays and single motherhood from existing as these are two of the biggest things that lead to kids getting raped/molested (and thereby continuing the cycle of becoming one themselves). How we do that is of course a lot of debate, but its the only real way to actually combat these things. Ending it before it even starts.