Do you usually break out your cell phone --- Cellphone??? Rarely carry one on a ride, and a lot of places I've ridden are so remote they don't have cellphone coverage anyway (i.e. many parts of the Canadian Rockies)
walk to the nearest bike shop and try to get it repaired on the road? --- That would be a bit of a hike.
Nearest bicycle shop is about 70 km away from where I live.
I rarely see any of you with backpacks --- Who would want to ride any distance with a backpack? How uncomfortable!!
so I don't know how you guys survive without any tools while out ont he road. --- What makes you think we don't have tools? What an odd comment. Have you never noticed that cyclists often have seatpacks, trunk bags, handlebar bags, panniers ... or if none of that, we've got jerseys with rear pockets?