Earlier quoted context omitted.
Alex is famous because he does "free soloing" - which doesn't use any ropes or safety at all. More people do "free climbing" which uses ropes just in case of fall. Anyone have any idea how often free climbers end up falling and needing their ropes? Could many good free climbers do what Honnold did, but just like the added bits of safety?
When people push difficult sport routes, they may fall fairly frequently. When doing an easier route, or if you are trad climbing, you really shouldn't fall. Should, or shouldn't, is all theory, though. Last year, a friend of mine who introduced me to climbing fell to his death on a trad climb. I don't know what happened, but I assume his protection equipment slipped out of where he placed it.
However, your statement about trad climbing is inaccurate. People project hard trad routes all the time, fully expecting to fall.