But I think it's better for it to fail from expected behavior vs unexpected behavior. Your storage being full is very transparent and expected, but that a file reaches max size and starts cutting off is unexpected and would surprise a lot of people.
I myself use supercomputers and the log files can get into a lot of GB, and I would hate it if it just cut off at some point.
Fun fact: German actually has a distinction between these two meanings of the same. "Dasselbe Schiff" would be the ship itself, and no other ship, even if it is the same. "Das gleiche Schiff" is another ship that is the same.