I always apply the brakes, but then I only have one child and one buggy - so having to leave it isn't really a scenario I'd ever be part of. In fact, I am possibly the only person that also wears the wrist strap - which even my wife doesn't. (You could argue that in some situations, this is more dangerous.. rather like a rucksack without the emergency release velcro).
I doubt the brakes were put on. Even though they're only on the rear wheels, they're pretty solid. I am sure the air pressure blast was strong, but doubt it would shift the buggy much (more likely tip it over).
However, I totally agree that buggies should have a permanent brake unless released manually design - although I suspect that could make pushing one for a long time a bit uncomfortable and people would simply not buy them.
Maybe another option would be to do with the wrist strap. Take it off, and it sets the brakes, but of course that almost certainly means some sort of powered solution.
Did the platform have emergency buttons on the wall to cut the power (or whatever they actually do)?
While I don't want to shift blame on London Underground for this, the use of barriers would be a worthwhile investment. Already used at many stations, they have another benefit in stopping people from blocking the passageways. A barrier, even if not designed for this incident, would have worked.
I wonder if there will be a subsequent legal challenge from the family on the basis that the lack of a barrier made LU negligent?!