Personally, I already lock up anything worth jack before going somewhere dangerous, so I treat it like a very real threat even when it isn't, but there's a couple problems that I see with the idea of this stuff.
The power dynamic that exists between assailant and victim is massive in these cases. Let's assume that the person who mugged you isn't in a group numbering four people or greater and is literally just a solo junkie. There's a 100% chance the person mugging you was wearing a mask, different clothes and a good chance they altered their description too - you are never finding them. Realistically, that's just how it is.
...But lets take it a step farther...
Even if you do find them, what now? Snitch and let the CP's know that this dude mugged you three weeks ago with no evidence? Let's say that they buy your story or that they somehow look deep enough to find proof, well now you've made an enemy. One that will possibly just be beaten once and then let go. Afterwards, they will then kill you due to escalation rules. Maybe kill them yourself, but that's a massive risk itself since you can get caught at any time or die in the attempt. Could forgo killing altogether and simply attack them back, but then you just end up in the situation where you're on the backfoot waiting for the likely lethal blowback.
Point is in these 'revenge' stories the victim is always on a massive backfoot.
That's the practical side of things. On a more 'fun-factor' side of things, I just cant imagine how being regularly mugged for your stuff is engaging, or capable of nurturing some blossoming story. If Willard players were a likeminded group of purely RP interested tale-spinners, maybe. But lets be real here that's not what Willard is composed of. The dude stealing the clothes off your back isn't doing it cause he's getting excited at the potential you may clonk him on the head with a frying pan two weeks from now
He's stealing your shirt cause he needs cloth to make some bandages.
(There's also the matter of the FearRP shit, which typically I'm fine with, but being forced to act like a mewling coward isn't exactly the greatest joy either in situations like this)
Beyond citizens, I'm pretty sure back in the day the rebel scene experienced loads of problems with people constantly stealing and killing eachother over scripts. I recall a point in time where rebels fought eachother almost as much as the Combine - I can't imagine mugging rules were too far behind on that measure. Maybe I am not remembering this bit right, but the above still stands regardless.
(There's also a side-issue of repeat offenses. Getting mugged multiple times over the course of your experience will get old fast)