If it signifies the end of time, then all the stuff in the black hole would need to no longer exist no? If anything is happening in the black hole, then time is still progressing, so nothing must be all that exists?
In a gravitational singularity spacetime breaks down. You could argue that time stops, but it’s also valid to argue that causality breaks down and we can no longer make any predictions about the future. Just because we don’t have a theory describing what could happen, doesn’t rule out that something could happen.