Indeed, people do reuse uncanceled stamps. This abuse includes both regular stamps and "precancel" stamps. These are examples from 2022. One cover confused the postal machines, causing the envelope to receive two postmarks, though neither in the correct location, yet it was still delivered.

Back to this thread's original questions:
1)
Does anyone know why this (lack of cancellation) happens? I think a variety of reasons have been stated above, including imperfection of the fast-paced processing system.
2)
How do folks handle the uncanelled-but-used stamps in their collection? I personally prefer a light cancellation on my collection's regular stamps, as that demonstrates that the stamp is indeed postally used. However, for "precancel" stamps, I prefer no cancellation as that is how they were intended to be utilized. Each person probably collects to his or her preference.