IMO, if you have belt showing, that tire was worn out some time ago. There are "wear bars" in the tread of the tires. When the tread gets down to the wear bars, it is time replace it. (A picture would help here, but I don't have one--none of my tires are close to the wear bars at the moment.) Especially, if you ride in the rain much.
In my experience, 12k miles is good for a rear tire. Most front tires don't last nearly that long. I know many on this list eschew Metzlers but I like them (not thrilled about the price, but...). If you get a flat with a cheap tire, they tend to come off the rim much quicker than Metzlers and can cause a crash. I've tested an ME-88, two up, in exactly that scenario. Other than the flat tire, no drama.
Tom