Instead, how about simply adding a maintenance system? So you have to clean the weapon every now and then. But bear in mind that weapons designed for military service are designed to go farther between needing cleaning. That’s why there’s a trade off in say, a battle rifle that most troops are issued. Sure, it can go longer between services but the trade off is parts designed to fit a bit loosely so it won’t be super accurate at long ranges. Where a sniping platform will be more accurate at greater range but you have to be sure the bore is clean more often etc.
As for jams, in most box fed weapons the magazines actually contribute to most jams. Feeding is a big issue and if a magazine’s lips get worn or bent (say, from dropping), then it doesn’t feed quite like it should and you’ll get jams.
Maybe just have a dirt/service indicator that changes colors? Green means good to go and then that changes through yellow down to red. When in yellow you might get a jam now and then. When it gets into red accuracy begins to suffer from barrel fouling and it will jam a bit more often. The longer it is let go the longer you’d have to spend cleaning it.
This also means you now have to look for a cleaning kit and spend some down time just cleaning the thing. How realistic do you want it? Will you have to sit down and field strip the weapon? Clean the mags and gas ports like you should? Need to pick up a few tooth brushes and rags along the way?
As much as I love 7 Days, the idea of weapon parts wearing out was insane. A weapon can go for thousands of rounds before it even gets properly broken in. Then, as long as it is oiled and cared for, it can shoot tens of thousands of rounds without magically just snapping in half one day or puking its guts out or some other rubbish.