As far as is publicly known, the failure has occurred three times, and has led to two crashes. It is possible to recover from if you know what you're looking for and you act promptly. However, Boeing did not tell pilots what to look for.
The pilots did not diagnose it as stab trim runaway because it's not stab trim runaway. When MCAS is malfunctioning in this way, it engages nose down trim for 9.3 seconds, and then pauses for 5 seconds. A runaway trim is where you have a stuck trim microswitch or relay or some sort of short circuit. You're expecting a continuous trim input. The confusing thing about MCAS is that it appears to resolve itself, but then waits 5 seconds and comes right back.
By the way, the wheels going clack clack is a normal thing at that phase of flight. The 737 has something called Speed Trim and another thing called Mach Trim that automatically adjust the trim as the speed of the aircraft changes. In the initial climbout, this will be running constantly.
Both the speed trim and mach trim systems are documented in the 737 manual and pilots are required to know how they work to get a type rating. The workings of MCAS were deleted from the manual before it was released because Boeing was concerned that the FAA would require more training on the system, which would cause Boeing to have to pay a contractual penalty to Southwest Airlines.
edit:
Also, Boeing's own test pilots failed to respond promptly to this failure in the simulator: https://aviationweek.com/air-transport/aircraft-propulsion/b...
It's very easy as a pilot to say that you would do a better job and something like this would never happen to you. The earth is pockmarked with the smoking holes of these people's airplanes.