Having been reading up on 1930s and 1940s aircraft, I can think of a few major problems that dogged the design back then.
Pushers had advantages of pushing the wings and control surfaces through undisrupted air and that gave enough advantages that the a lot of pusher designs were put forward. A pusher would have superior cruising speed and better wing loading because it flew through undisturbed air.
The most successful was probably the XB-42 mixmaster which would have been deployed had the war gone on. (As it was, it it eventually deployed as America's first jet bomber.)
The B-36 used pushers precisely to give its wings a clear airflow. It was actually designed in 1942.
But they had big tradeoffs.
A major problem with pusher designs of that era was cooling the engine on the ground.
With a tractor (puller) you have this giant fan running blowing air over the plane and the engine (air cooled radial) and/or radiator (water cooled.) With a pusher, the prop just blew air behind the plane, leaving a powerful engine with nothing but passive cooling.
During a crash, a tractor engine in front served as a crumple zone for the rest of the plane, particularly the cockpit and could plow through obstacles making the plane come to a halt slower. Conversely, with a pusher, the engine was behind the pilot and not only didn't offer any protection but tended to tear loose and ram through the rest of the fuselage like a pile driver.
The pilot could not see and therefore visually inspected the engine e.g. if you start loosing oil in a tractor, you know right away. If the engine is behind you, you might not notice until you see the gauge.
Center of thrust was more difficult to balance and that made center of gravity tricky as well.
Still, with all these disadvantages, XB-42 and B-36 showed that the advantages could be come out on top with enough good engineering. And in the end, jets work at least half by pushing. If jets had be delayed a few years or the war had started back in the mid-30s, we probably would have seen more pusher designs in service.
With jets, the military need for pushers disappeared and in civilian aircraft, there is seldom much need for an increase in performance that justifies fighting all the tradeoffs.