Instead of weapon degradation I'd like something a little more realistic. I'd like for weapons parts to have grades of serviceability. Something like broken, badly damaged, damaged, worn, like new with stuff that's like new being much rarer with the difficulty/intelligence of the enemy affecting the drop rate. The leaders of gangs are obviously going to have the best equipment but that means they have the best equipment so they are going to be harder to kill. You also wouldn't expect a super mutant to take good care of his weapons so it'd be rarer (even for the boss) to have decent weapon components. On the other hand they probably have the best melee weapons. Then you can strip weapons of their components and salvage the good ones while scrapping the rest. Eventually you'd be able to assemble the best version of your weapon.
And that'd be all well and good if it ended there. But I'd also like it if they added a small, very small, chance for something to break. Maybe a spring or a firing pin snaps, maybe you use your gun as a melee weapon (exponentially increasing the chance of breaking something as they aren't meant for melee unless you have the proper upgraded components and still a much higher chance of breaking something) and the stock is damaged, maybe your barrel warps after firing hundreds of rounds. Maybe your sword snaps in twain after beating a particularly thick-skulled super mutant over the head with it The chance of breakage could also be affected by the amount of care you give your weapons.
In addition to not using your gun as a melee weapon maybe you have the option of sacrificing a few hours of sleep when trying to rest (this could tie in with the new hard core mode) and break down and perform some maintenance on your weapons. You'd need a repair kit that you would need to keep stocked and some components (varying based on the weapon). The more often you do this the less chance something breaks and vice versa. This would also necessitate a backup weapon or two. A pistol and or knife if you are trying to keep weight down maybe.
This would add a certain degree of realism and make people think about what they are doing a bit. Do I want to charge in guns blazing, are my weapons in good enough condition I can rely on them or might they break in the middle of the fight. Do I want to wait a bit and see what happens, maybe sneak through or lay traps instead of relying solely on my weaponry? It would add a degree of danger to what might otherwise be just another boring waltz in and blow everything to chunks. And maybe if you are severely unlucky and haven't been doing the due diligence that any unlucky person knows they need to rely on, your weapon might catastrophically fail and damage you instead, but you would need less than average luck and poor weapon condition and/or poor weapon components. The more of those you have the more likely it is to do so.
TL:DR
Varying grades of component condition
Small chance of something breaking
Preventative maintenance
Oh [censored] factor
Hmm, seems a bit of this has been said already, sorry was ninja'd for some of it but I hope this is at least a bit more comprehensive than having to follow an argument.