I never got the feeling Calvin was lonely. I grew up with a brain a lot like Calvin's (without the desire to get into trouble, though). School and the other kids were an endurance and being alone was a LOT more fun. Other kids intrude on your imagination.
In one of his compendiums, Watterson explained that early on he wanted Calvin to interact with other kids, which is why he once went camping with a bunch of Cub Scouts. Watterson decided that Calvin wasn't the sort to join in group activities so he dumped the concept.
Calvin had his own sports. Who can forget "Calvinball"?
"NO sport is less organized than Calvinball!"