Actually, it does hurt. It does hurt to ask the wrong way, to ask without preparation, to ask without permission. It hurts because you never get another chance to ask right.
If you run into Elton John at the diner and say, "Hey Elton, will you sing at my daughter's wedding?" it hurts any chance you have to get on Elton John's radar. You've just trained him to say no, you've taught him you're both selfish and unrealistic.
If a prospect walks into your dealership and you walk up and say, "Please pay me $200,000 right now for this Porsche," you might close the sale. But I doubt it. More likely than not you've just pushed this prospect away, turned the sliver of permission you had into a wall of self-protection.
Every once in a while, of course, asking out of the blue pays off. So what? That is dwarfed by the extraordinary odds of failing. Instead, invest some time and earn the right to ask. Do your homework. Build connections. Make a reasonable request, something easy and mutually beneficial. Yes leads to yes which just maybe leads to the engagement you were actually seeking.