Thesis: Graverobbing is extremely uncommon in Noxus because people generally aren't buried with anything valuable _and_ left unguarded.
First of all, Noxus Prime doesn't have a whole lot of space to bury people _ in._ I'm sure some of the noble houses have family crypts, but your average middle-class schmuck isn't going to have a whole lot of room if they want to bury Grandma. Most people in the city would probably get cremated to save on space. Noxus _does_ have a whole lot of land that can't grow anything, so it's possible you'd get some proper graveyards further outside the Bastion.
Secondly, Noxus has a well-deserved reputation for brutal pragmatism. Why bury Grandma with her favorite quarterstaff? What's _she_ going to do with it? Better to keep it in the family so someone else can make use of it.
The nobles with their fancy family crypts might bury people with stuff, since they can afford to have people guard said crypts. We know Sion was interred (briefly) in his own monument, and they probably put his ax in there, too. But the looting risk would still be pretty low since you'd need a team of multiple thieves and an oxcart to get Sion's ax anywhere.
Well, that's pretty much it on my end. Feel free to add your own ideas and theories.
(I know Realms of Runeterra is coming out TOMORROW, so it's very possible a lot of stuff in this post is going to be proven wrong. But I'm not going to let that stop me.)