A simple answer: there's a reason California is the "land of fruits and nuts." Its the furthest West you could go so it ended up full of weird religious groups, entrepreneurs, LGBT people, and so on. (People on the West Coast are now building spaceships because it's not far West enough?)

Of course the American West was not a pure frontier. It was already populated, so pushing West involved displacing other people. Space on the other hand would be a pure frontier, something that hasn't really existed on Earth for thousands of years.

A better picture of what you might get with a pure frontier would perhaps be Polynesian culture before colonization when they hopped from largely unpopulated island to unpopulated island. It would be more peaceful than the American west, more focused on exploration and settlement since there would not be conflict with existing occupants. Conflict between settlers is not even very likely due to the sheer amount of empty space.

You could argue that in the far future we might meet some aliens, but I'd counter that space is so f'ing huge that conflict between even massive civilizations would be unlikely unless it were driven by irrational motives.

"It's called space for a reason."