My answer: It depends on the circumstances.
Before someone jumps to conclusions, and accuses me one way or the other, please hear out my explanation.
Some yudansha (mostly kids, but I've known a couple of adults that did this) will attempt to get the beaten-in, weathered look artificially, by repeated washings in hot water, in combination with harsher detergents, and even a touch of bleach. Others will try to drag their belts across rough surfaces, or even (sadly) take a rasp / file to it. Still, others will try to use a blade to cut various areas. I really, really frown upon this, since such efforts could simply be better used towards one's training.
Now, some belts are more prone to wearing out than others, and if a belt looks a bit weathered just after a few years through regular training, sometimes this is unavoidable. One of my black belts is made by Tokaido, and it seems that the black dye they use in the belt, tends to bleed out a bit too easily, even though it has been less than a year that I got it. Still, the belt is in great condition, and none of the seams are broken, or the edges frayed, etc.
Other times, though, some belts, especially the 9 dollar satin ones, will fall apart all too easily, through no fault of the wearer.
When someone gets their black belt, I would hope that the chief instructor granting the rank isn't going to buy those el-cheapo belts that fall apart too easily. It really is worth it to spend 25+ dollars to buy a good brand of belt (Shureido, Tokaido, despite the dye problems, Pine Tree, etc).
In general, it's pretty easy to tell who the wearers of the tattered belts are,, in terms of skill level. One such exception, I will describe below.
On a rare occasion, some new yudansha, however, are given an old belt from their instructor, in which case, it's an honor to wear such a belt. If someone criticizes the wearer, the wearer should simply tell the truth, and that's the end of that.
Now, on to a slightly different topic of belt care:
If your belt starts smelling badly, it doesn't harm the belt if you occasionally put it in the washer, using a cold cycle, gentle speeds (this is VERY important), and a mild detergent that is designed to preserve colors, such as Cheer for dark colors, etc. Let it drip dry (do NOT dry in the dryer; this creates more wear and tear in the negative manner that I explained above), and it comes out clean.