Necessary? No. But its something with a long history and was the original approach. And keep in mind, there's a difference between being a "loner" and being "mopey." Batman is mopey, but he's not a loner; just look at how many sidekicks, partners, friends, and peers he interacts with on a daily basis. He pretends to be a gruff, lone-wolf but his actions show that he's built a family around himself and even though he might be an emotionally abusive ass to them on occasion, he keeps them close. Superman by contrast, is friendly and approachable, not mopey at all, but has a very small circle of friends; most of whom don't know his secrets or, if they do, have little interaction with his "other" side.
But no, its not necessary that Superman be a loner, and there have been some successful versions who were decidedly not.
Again, not necessary, but built into the original history with decades behind it. It just comes down to personal preference, really.
And tragedy is a part of Heroic Journey and has been since the Greeks at the earliest.
Just because bad things happened in Clark's life doesn't mean his story is just tragedy; its about not letting those bad days define who you are. It's the exact opposite of "tragedy" because even though Clark has suffered, he rises above it. Personally, I find that infinitely more inspiring than a Superman who has never *really* had anything bad happen to him.