No.
however, let's examine what that might actually look like. Just for funsies.
So, first we need to understand why this happens, in the fiction of the game world. Because it is happening due to the PCs leveling up, let's make that the reason in the fiction too. That means that leveling up is a thing that happens in the fiction --- which itself presents all kinds of interesting situations and stories.
Anyway, the PCs have leveled up and the world responds by getting more dangerous, at least where the PCs reside. Regular thunderstorms are replaced by Mana Blizzards and whatnot. The farmers and stuff that live in the area suddenly have to deal with deadly environmental effects -- and they know exactly why. Higher level or not, the PCs are now on the bad side of the local population. "Adventurers bring trouble" is brought to a whole new level. The farmers can't run the PCs out of town, but the local lord might be able to. Or, more likely, send the PCs off on a long question to get them out of town for a while, at least.
Now the question is: does this heightening of the world's dangers follow the PCs? If the random encounter/event chart scales, then it makes sense that int he fiction it does. There is a bubble effect around the PCs, warping reality and bringing trouble with them. Villages along their path can feel their passing, as the occasional raiding wolf is replaced by dire worg packs, etc.
I rather think this would be an interesting and fun sort of world to play in.