The agreements put in place regarding the partition of authority over Germany after the war did not require keeping the roads and railways open, but did require keeping air access open along certain corridors.

So the East/Soviet leadership was able to close the roads and railways without violating any agreement; the Western/US/UK/France leadership had simply not anticipated originally that this would happen.

There were documented cases of harassment of planes, but shooting them down would have provoked another war immediately. And the Soviets knew they were not prepared to fight another war. Especially because the Soviets did not yet have nuclear weapons at the time of the blockade/airlift (the blockade lasted June 1948-May 1949, and the USSR did not conduct its first successful nuclear-weapons test until August 1949).

Nuclear war?

The same forces that prevented active warfare between the superpowers throughout the Cold War period. It came down to how much provocation they could get away with. In the case of the blockade, preventing ground traffic was doable but shooting down airplanes would have rapidly led to an all-out war.