It's just not as good a choice considering the other options.
.
Biggest issue I can think of now, are if you adjust chain tight enough to eliminate backlash, then you'll get binding, so you always need to run with a bit play otherwise you'll get accelerated wear. It also needs lubricated, which generally leads to dust/dirt sticking to it (I know there are dry lubes available, but you nearly always get left with some form of sticky residue). And they need regular adjustment.
.
Ultimately, belts are usually easier to implement, and longer lasting with less maintenance needed, for similar money.