Why is the first axis of STFT frequency bin
It is really a matter of convention of the communities that use STFT. Medical devices tend to have time scrolling left to right or over writing left to right. For passive SONAR, most displays that Im familiar with have time water falling down and frequency increasing from left to right. There are exceptions as well. I've also seen amplitudes as marching mountains, color coded, and intensity coded as well. Much depends on the amount of time history that should be displayed and the time duration of signal events that are of interest.  There are also perceptual consideration based on human vision that come into play and effect how STFT data is displayed. There are also places where an STFT display is the input to image processing algorithm.