Did Gollum deserve death?

[HerenIstarion]

So the effect of just punishment would, in the end, only be to satisfy our sense of justice, which is little. It's difficult to say whether a combination of punishment and healing, like in an asylum, would have had a effect, but I have a feeling he wouldn't have accepted healing from his punishers

Tread gently, for you are treading dangerous soil here. It seems/feels to me that Gandalf's words as quoted in the opening post contain layers of thought, not just what can be read at first glance. "Can you give what is deserved" indicates also (it seems to me) imperfection of the giver of the deserved/undeserved.

(Cf John 8:7 So when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her)

For healing as I read it out in your post may be easily substituted with changing and that in turn with moulding of a person, and whose mould is good enough for the task?

As for Frodo, his very being in the same boat must have played the part. If there was no Gollum to look at and antagonize and sympathize with at the same time, [I feel] like Frodo would have fallen sooner.

(It's a frenzy of quick typing out of whatever is being born in on me, I hope you follow)