You may be expecting far too much of your government. My opinion is that if pedophilia became a mental illness treatable by execution, enemies of the powerful might discover that their hard drives had been filled with outlawed images without their knowledge, rather than just having convenient car wrecks or drug overdoses.
Why just murder someone when you can simultaneously discredit and vilify them?
If you truly believe that such people are too dangerous to live, the logical course of action is for you to go out and murder them yourself. Are you prepared to deal with the consequences of that? Would it be better to just hire a professional to do it on your behalf? Would that become more acceptable if the professional is a state employee?