Wrt the 2/4 ... yes, I get that when you have a single kick and a single snare hit BUT ...
Counting in 2/4 is cumbersome and makes it difficult to keep track of where you are wrt the melody and I very rarely count in 2/4 (when I need to count). In addition to keeping time, it is kinda' a drummers responsibility to musically indicate the end of one phrase and the start of another (e.g., the crash cymbal on beat 1 one of the chorus).
If I need to count because a piece is unfamiliar, I will find a time signature scheme that leaves me in the right place at the right time.
Also, notation, time signature and what you do in your head may differ ... and what 2 musicians count when playing the same piece may differ.