A big reason of why I train martial arts is so I don't have to give my money a would be mugger and run.
As always this age old ''awareness&avoidance'' is pretty and all but just like you said yourself cxt trouble can find you anywhere. And I would say the trouble that finds people that actually are aware and avoiding can be a lot more dangerous than the typical drunk fight.
This question of why/what is martial arts and to defend yourself or not to or only to as an absolute last ditch effort is a seperate argument.
But in terms of ''price to pay'' that is purely individual... Self defense is more intent than technique. That being said technique is still absolutely necessary but the rate at which someone learns technique differs not only based on the time they put in but their ''talent'' as well.
Not to mention the efficiency of the training.
Also I feel a lot of people gravely misunderstand something when they think that 3-5 hours of training a week in a class with 1 instructor is their path of learning martial arts. It takes a lot more hard work than that to really get effective, wether in sport or self defense.
I don't think you can measure the price.. People are different and there is more to self defense than your ''fighting skills'' also the mental side of it you can't really learn in a class room.