In 1984 a Mark 2 DBSO leading a train of five Mark 3s propelled by a class 47 hit a cow at 85mph at Polmont, and derailed,
killing 13 people. The aftermath of this led to the DVTs for Mark 3 stock on the west coast (now mainly on the Great Eastern, but also on the Chiltern mainline) and the Mark 4 stock on the East Coast being non-passenger carrying, and I think they're ballasted too?
However, there hadn't really been a problem on the Southern network, where various push-pull formations had run for many years- the Weymouth service for instance used "4TC" unpowered "multiple units". One or two of these were pushed from Waterloo by a powerful 4REP unit to Bournemouth, from where they were hauled to Weymouth by a class 33 and then pushed back to Bournemouth.
More generally, most older EMUs (including designs built into the late eighties such as 317-322, still running) used a single powered car in the middle with two or three trailers- so are always running with one or two trailer cars being pushed.