It seems to me that Elves are never really alone. Think of Legolas when he waited for Aragorn and Gimli to get enough sleep. He was communing with the stars, reliving memories as if they were real. Arwen could commune with whatever natural things there were around her, and, of course, with other Elves at Rivendell and Lorien. Her true loneliness came when Aragorn died. She had cut herself off from all other Elves, and had nothing left but her husband and her children. No wonder whe gave up her life.
Gollum wasn't merely lonely. He was ostracized, isolated, cut off from everyone else already (except for Deagol), and the Ring only made this worse. At least Frodo always had Sam, though, as you pointed out, to bear the Ring is to be alone.
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