Why don't planes have a reverse propeller as air brakes?
Planes with a variable pitch propeller can have a pitch range which twists the blades such that they provide reverse thrust. This started to become a common feature on high-performance airplanes in the 1930s.

Not all variable-pitch propellers can produce reverse thrust, however. The constant speed props on small propeller aircraft usually don't, because the energy of the plane after touchdown would be too small to justify the added complexity. On big airplanes which need short landing distances (the C-130, for example), they are a standard feature.

In 1936, Heinkel produced a sleek dive-bomber, complete with retractable landing gear and a reversible pitch propeller which could be used as a dive brake. The He-118 was test-flown by Ernst Udet, who did not pay attention at the briefing and went on to overspeed the airplane in a dive, destroying the prototype in the process. Thus, the clumsy, fixed-gear Ju-87 was chosen to be the "Stuka" and the He-118 would end as an inspiration for Japanese aircraft designers.

The Pilatus PC-6 Turbo Porter is a favorite with skydivers because it can put the propeller into reverse even in flight. This allows for spectacular descents and enables it to be safely back on the ground before the skydivers it dropped a moment before have landed.

As usual, Wikipedia covers the topic well, so here ist the link.