Literally the definition of the integers is that (x + 1) != x. Wrapping is bad enough, but at least tends to makes failures noticeable. Saturating arithmetic makes it really hard to see that a failure has occurred.

Depending on the performance penalty you're willing to take, there's good alternatives to wrapping, such as: A) 64-bit integers, B) bigints, C) crashing on overflow.

Sure, saturation might be useful in certain circumstances, like manipulating audio samples, but it's generally something you want to make explicit. Using it everywhere? It's madness!