From a collaborative standpoint a GM has a responsibility to handle character connection during character creation. Although it is possible to have a scenario where everyone meets each other for the first time, its usually better to start in medias res or as far forward in the story as you can.

Characters choosing to start away from the party or who play DARK EDGY LONERS are usually just rejecting the premise of a story. From a literary stand point it might be possible to have widely separated characters working towards some common story goal, even possibly never meeting, but the collaboration in such a chase would have to be thematic or world building rather than character interaction. I might write a story where a barbarian's struggle in the wilderness parallels the barbarity of 'civilized' life but unless this impacts the other characters in some way, people would need to be really bought into the premise for anyone to ever care.