I think all recoveries carry an element of risk, that's why we take care to make sure nobody is in the firing line. We know a winch rope has just as much potential to do some serious damage.
I think you're probably right and if you have the option to winch out of mud it might be the better choice but a correctly used snatch would be just as viable and safe/carry similar risks.
I think the likelihood of this kind of damage to a windscreen would be very low. Using the strap as intended (straight pull) will see the bulk of its mass recoil directly towards its fixture points if it does break.
If anything I think that these pictures and experiences are a lesson teaching us to replace our snatch straps a bit more regularly?