Your scalp is way thinner and much more delicate than the skin on your cheeks and neck. And remember that you can't see the back of your head, so you have to spend extra time shaving that part of yourself because you have to do it with two mirrors.
I shaved my head for a solid year, and I had to be incredibly delicate because any nick or scratch and I would bleed like a stuck pig.
But if you're shaving all the hair off, what do you need to see? Maybe I'm weird, but I could do everything except the parts close to the actual hair I wanted to keep without looking at it.
Sounds like cheap razors to me. Get a high quality razor + shaving gel and you'll never cut yourself. I've been shaving my head for 15 years and only bled once, from a crappy budget singly blade razor.
I was using a double-edge safety razor with my preferred blade and shaving cream. It's difficult to shave that part of my head because it's incredibly delicate. On the contrary I've gotten nothing but crap shaves from the cartridge razors.
Shaving is something where you really REALLY have to test different things to figure out what works for you. For example some men really prefer Feather blades because they can get a really close shave with them. For me, those blades actually tear up my face to the point that I break out in a rash. Using the same technique and a Gillette Platinum blade I can get an incredibly close shave in two passes.
Depends a lot on your skin. I don't shave my head, but I'll not infrequently get little nicks when shaving my face, despite trying all manner of razors, gels, and creams. Best is if I can give it a few days between each shave -- it tends to be much worse if I have to shave on consecutive days, as it's still irritated from one day when shaving the next.
I shaved my head for a solid year, and I had to be incredibly delicate because any nick or scratch and I would bleed like a stuck pig.