The brain does not allow it.
Even during sleep, the brain continues to analyze sounds, and a person can wake up if the sound heard is unexpected or has special significance (for example, a phone ringing or being called by name). A person can also wake up due to silence, for instance, if a night train that regularly passes by their house at the same time suddenly does not pass.
At the same time, a loud but familiar noise does not cause concern, which is well known to those who have fallen asleep on the subway. Thus, the brain of a snorer does not perceive their own snoring as an unexpected sound.
However, people with heightened anxiety or those who are trying to stay awake may wake up even from their own snoring.
