Adventure Time
Adventure Time feels like a very lonely place, and I don’t think that’s happenstance.
Adventure Time takes place in a world where everyone is unique. Everyone is created in some special way and shape, special made for the specific destiny of being themselves. Finn the Human is called Finn the Human because he’s the only one around – possibly the only one left in the world. Jake the Dog is, similarly, nearly the only dog we ever see – and the few others aren’t much like him, with his extraordinary powers. It’s that way for everyone, though: Everyone in the land of Ooo is one-of-a-kind.
Everyone is an island.
This feeling of isolation isn’t actually that unusual in children’s entertainment, though it isn’t usually quite this poignant. The people who created this stuff tended to be creative children who have since grown up, and creative children tend to be…
…lonely.
The cause and effect could go either way. Maybe they’re lonely so they become creative, maybe they’re creative so they live in the kingdoms of their mind. Probably both, playing against each other. Thus Where the Wild Things Are; thus The Binding of Isaac; thus Alice in Wonderland.
The inhabitants of Ooo all want to be closer, to find friendships and romance, but they’re usually too different to really ever be comfortable together. The most overt example is the relationship between Finn and the Flame Princess, who will literally destroy each other if they get too close, but it’s the same between everyone. Everyone stays alone.
They deal with this in different ways. PB devotes herself to work, to constructing a functional society and maintaining friends to keep her company, though with her authority she can never get very close to them. Marceline dedicates herself to art, to expressing herself and affirming her existence by codifying it into song. The Ice King is certain that if he just finds the right person, he won’t be lonely any more.
The secret is, it’s not really that unusual. We’re all unique, we’re all alone: Even at our most intimate with one another, we’re still cursed and constrained by our individuality. Loneliness is never something that completely goes away, just a sensation that grows and shrinks based on sensitivity and proximity. We’re humans just like Finn: We seek excitement, we seek companionship, we love our friends but usually don’t really understand them, and we’re lost in a society of people who are kind of like us, but not really the same.
But, if we must be alone, at least we can be alone together.
Problem Machine 
Interesting analysis. I agree with your conclusions about never really understanding the friendships we seek, and about the different ways we deal with loneliness. That show is brilliant imo, and succeeds on so many levels. One of the most creative ones around.