Many of us *are* hit with a baseball once a month.

Both recent and ancient; people have gone back and forth between rehabilitation/disincentive as punishment's goals for millennia. Look at confession/penance and the theologic justifications for that. Various penalties described in Ancient Rome and the Old Testament filled either or both those roles. We've had phrases like "teach him a lesson," "now, this is for your own good," and "spare the rod, spoil the child" for quite some time.

I omitted some details to simplify things. But now let's enter into full Tolkien geek mode! Unfortunately I gave away my Tolkien collection years ago when I realized how un-humanistic it was, so I can't provide quotes and page numbers, but I do rely on my memory.

The people of Numenor had been wanting to stop dying for several generations

True - I omitted this part to make things simpler.

he made him think the proper way to go about actualizing this was to worship Melkor (essentially Satan), do human sacrifice in his name, and go about conquering the world, including the land of men

Not quite. He made him think that to be immortal he had to go to the land of the Valar and possibly fight them. I don't remember if it's stated explicitly what purpose the human sacrifice had. And conquering the world was something the Numenoreans had been doing for generations, without Sauron, and anyway it's hard to see how they could have expected that to grant them immortality.

Also, it's explicitly said that Men did NOT become immortal by stepping on the Western Islands

That may depend on what version of the Alkallabeth you're reading. I don't remember which version(s) this is, but after Eru caused the Downfall, the punishment of the King and his army who had disembarked on the shore of the Undying Lands wasn't death. They were "imprisoned in a cave beneath the earth", IIRC, and there they would not die until the end of the world and the Last Battle.

In other words, they became so immortal that even Eru couldn't kill them, although he killed everyone else in Numenor...

Yes, of course, I realize this is reading out of context. Firstly it's an older story left from before the legendarium became much more explicitly Christian. And second it makes no sense for Men to become immortal just by stepping on the shore of the West.

But considered as a legend told by later Men, it's illuminating.

The Elves and Valar indeed said to Men, that Men would die faster if they went to the Immortal Lands, like moths burning in too bright a fire.

And you believe them? They're obviously speaking in their own self interest :-) Incidentally, these are the same guys who said that they had no idea what death was for, except that it must be good for something since it was a gift of Eru.

The Light Elves and the Valar are an evil, immoral bunch who never helped others when they saw them suffering. They abandoned Men for the first several millenia of their existence to Melkor (and later Sauron), and then blamed Men for "falling". Later they abandoned all non-Numenorean Men to Sauron, and then blamed them for becoming "corrupted and evil", and supported the Numenoreans in enslaving them. All this was before the Fall of Numenor, so they hadn't had the excuse of the West being "removed from the circles of the world".

The "righteous" weren't righteous by "saying they wanted to die"

It's the ideal. As you note, Aragorn and some others (e.g. the early Kings of Numenor) actually achieved it.

Later men were lesser men, in keeping with the story. But I'm pretty sure someone like Faramir would say that anything done by the early Numenoreans must have been right, and would claim to want to want to die on that basis.

The righteous, the Elf-friends, were primarily "righteous" by not engaging in human sacrifice, and by not supporting the wars of conquest.

True. And I expect they also kept saying they wanted to want to die without protest in old age.

I think Tolkien is actually pretty sympathetic to those people that desire immortality (as long as they DO NOT go about killing other people to ensure it)

Where do you see even a hint of this?

The Nine Kings of Men who were given rings by Sauron became immortal - and became Ringwraiths. It's implied pretty clearly, in Bilbo's descriptions of the One Ring (he felt "spread out like butter over too much bread", i.e. had lived too long), that this is partly due to becoming immortal in itself, and not just due to being dominated by Sauron's will. Orcs and Southrons were dominated by Sauron's will and weren't wraiths. And the Nine Rings did not AFAIK confer "trivial" invisibility as did the One Ring.

he even has Arwen not being cool over Aragorn's death

Meh. She chose to became mortal to marry him. She was angsting over her own impending death. After he died, she willed herself to die just a year later - explicitly in despair. And before that, her father and family never really accepted her choice, and they "parted in bitterness", i.e. fought and never made up. Hard to say if Tolkien was sympathetic, but other people in Middle-Earth definitely weren't.