Plus, if birth is suffering, suppose non-existence is free from suffering. I can't see any difference between the end of one's birth and the end of one's existence?
From my understanding of the suttas the point is to stop giving birth to "I am", that is to stop clinging to, and identifying with, that which changes, causes dukkha and is not self
When we do that there is the deathless as there is no identifying with that which ages and falls apart (body, feeling, perception, thoughts and counciousness) "you" aren't reckoned in terms of that (body, feeling etc) ... I am not that, this is not my self etc
It seems what you are doing is identifying with the body, or feeling etc and taking a view of annihilationism. That is when this body ceases, "I" will cease, and taking Buddhism at aiming at that, which it isn't
Your view of death being an end is also not self, as are all view points and opinions