If your blood didn't clot at all you'd probably bleed through your eyes and other parts of your body and within your body tissues and die instantly. (disclaimer I'm not a doctor or a pro and accurate info is hard to verify but that's my understanding) No paper cut needed!
Not really. Otherwise you'd have blot clots around your eyes, your fingernails, your hair follicles, etc. Our blood is held in by our body naturally. Much like a garden hose, you need a rip or tear to start a leak.