I'm not sure any good engineers really believed it was a true "speed limit" for atmospheric flight. They did know that when you approached the speed of sound with aircraft (as was not unknown in a dive, for example), the turbulence usually resulted in the craft crashing. To build craft that could easily and routinely go faster than the speed of sound required very careful engineering that minimized the turbulences and maintained stability. The fact that most craft were not built for those kinds of turbulences means that people who went those speeds in a craft would have a bad time of it. You can see how many differences went into such engineering by comparing the fighter aircraft of World War II with, say, the Bell X-1 (basically a rocket with wings), much less modern aircraft designed to fly for long periods at supersonic speeds (e.g. the Concorde or the SR-71, which look really different from a lot of what came before them).

(Imagine accelerating a VW Bug to Formula 1 speeds and trying to keep control of it. The aerodynamics would be terrible, the weight distribution would be terrible, the friction of the tires would be terrible, you'd spin out and crash in a moment.)

To put it in another, tautological way: sub-sonic aircraft were not built to go faster than the speed of sound. Traveling at speeds of Mach 1 or greater requires different aerodynamic considerations if you want the craft to stay stable and controllable. (The fact that Mach numbers are named after a 19th-century physicist — Ernst Mach — should indicate that nobody actually thought that the speed of sound was a true "speed limit" for movement in an atmosphere — physicists and engineers had long known that things could break the speed of sound and that it produced interesting, complicated shock effects.)

As an aside, I was curious whether the term "the sound barrier" was actually common prior to it being officially "broken." Google Ngrams suggests it was not — that "the sound barrier" became something that was written of primarily after it was "broken," not something that people wrote much about during the time it was supposedly regarded as a "barrier."