It is one of the few advantages of having amplification. You can turn it off.

Running over is either incompetent or rude or both.

My daughter's first rock band were LOVED by the pubs they played in because they ALWAYS rehearsed the set with introductions and timed it and the pub could be SURE that they were not going to get legal problems because the music ran on late.

When timing your set in rehearsal, remember that introductions end to get longer in a live setting and also that the songs tend to get played a fraction faster.