Yeah, we teach it. It ends up showing up again in measure theory, assuming that anyone still bothers to teach the mostly useless Lebesgue integral instead of the gauge integral. Measure theory shows up again in probability theory if you're not using Kolmogorov for some sadistic reason and you have to deal with countability.

Otherwise it's pretty much a dead end unless you're in the weeds. You just mutter "almost everywhere" as a caveat once in a while and move on with your life. Nobody really cares about the immensely large group of numbers that by definition we cannot calculate or define or name except to kowtow to what is in retrospect a pretty bad theoretical underpinning for formal analysis.