I don't have hard facts, but my guess is most contemplate hand propping after leaving the master on over night, not mechanical failure. In most of our airplanes, if your battery is dead, you have no alt. current, no charge, no electrical. In most of our airplanes, no electrical means you are not even going to consider going anywhere unless it is a true emergency.
I have propped a few 0320/0360's, usually after enough charge was put on the battery to get the alt. alive. It is not my favorite thing to do, but I wouldn't say it is necessarily "difficult".
I propped my old L3 without any electrical system hundreds of times, for many years, cause that is what you do. Of course, it was only 65hp, which is just enough to kill you.
A lot of thought goes into it before I ever consider a hand prop. It is very dangerous and the engine and prop hold no prejudice or forgiveness.
Smart People do Stupid things all the time. I know, I've seen me do'em.
RV6 - Builder/Flying
Fiat G.46 -(restoration in progress, if I have enough life left in me)
RV1 - Proud Pilot.