An interesting hypothesis.
The 'doom' of men was to leave the world for they were not bound to it. The Silmarillion tells us that their mortality was the gift of Eru (that, in itself is a whole other topic) so it was certainly against their nature to be immortal while in Middle Earth. Weather or not they had an afterlife different to the life of Arda, we know not and can only speculate.
Let us assume, for argument's sake, that there was some kind of afterlife for men after they died in Arda. Logic dictates that this would be something they would be more adapt to, else they wouldn't get it; they can't live indefinitely in Arda because they are not adapt to it. To ask weather or not it would be better for them not to exist or such is a question we cannot answer because we do not know what it would be like to not exist and so have no point of comparison.
Melkor's coming distracted them from this, yes and you could argue that the reaction of the Numenorians was proof that Melkor's distracting them was a good thing. But then one could argue that the other races upon Middle Earth seemed much contented (including the Dwarves, but that is a different subject).
In short... I don't know.
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