I think our belief in self-starting, rugged individualists got started in our frontier society. Anyone who was willing to slaughter a few Indians, or talk the Army or militia do it for him, could start his own farm, and if he worked hard enough, make a go of it (particularly back East, where the farmland was productive without irrigation). Or he could start cutting every tree in sight and get rich in the lumber business -- no one to stop him. If he wanted to start a mine, the gov't made it absurdly cheap and easy to stake a claim and acquire mineral rights -- hey, there was plenty to go around! The advancing frontier meant a constant influx of new land, new mines, new forests, new opportunities, while the growing influx of immigrants provided cheap and abundant labor, which opened up all manner of opportunities for robber barons to flourish. Once the frontier was closed, things were bound to slow down, and as the "empty lands" were settled, things slowed down even more. The endless expansion of opportunity is not there anymore because the mechanisms which provided it are not there anymore.
Making your way in a society where every niche is already occupied means competition becomes a factor in a way it never was before. You can't just move on to new territory and start over anymore. But our mythology has never caught up with the facts.