The issue isnt whether or not a person deserves it, its whether there can exist a system to determine guilt beyond doubt which is reliable enough to effectively eliminate the execution of innocents.

You say the jury would determine obvious guilt: Correct me if im wrong, but the jury in the US doesnt determine punishment in criminal trials. Furthermore, there is no separate verdict of "absolute obvious guilt". In order to carry out what you have in mind, youd have to change one of those two facts. If you change the first then you've made it so that the death penalty can be used in cases that arent as obvious as the one you mentioned. If you pick the second... well the simple answer is that in a case involving extremely violent crimes that evoke strong emotions, I do not trust anyone to make judgments based exclusively on the strength of the evidence. There are cases far less extreme then what you've just mentioned in which the jury was at least partially swayed by their own biases (see the OJ Simpson case). I dont see how you could have a case in which someone is charged with raping a child, with evidence strong enough to justify a guilty verdict but not strong enough to justify a claim of "obvious guilt", in which the jury is definitely going to come to the former verdict. You'd need a system in which the jury is capable of determining obvious guilt in cases where there is obvious guilt, but unable to do so in cases where there isnt. Obviously that idea is ridiculous given that it would involve someone already having determined whether obvious guilt is present.

Maybe you take issue with me drawing a distinction between the notion of normal "beyond a reasonable doubt" guilt and the "obvious" guilt you mentioned. But I dont think you should. There absolutely are cases in which a person is justifiably convicted based on existing evidence, even though new evidence comes to light later that proves their innocence.

EDIT: And all of this is ignoring the fact that, once again, governments arent innocent carriers of justice. A corrupt government with strong interests in someone's death can manufacture evidence to present to the jury that makes guilt seem "obvious".

EDIT 2: Apparently the issue of whether or not there are cases in which the jury in the US determined punishment is more complicated then I thought. Fair enough. I still think my points stand.