How often you tap your foot and what the time signature fraction means in terms of beats per measure is not always related.
I play with a big band and we often play music in 4/4 time with tempos above 180 bpm.
You're not going to tap your foot four times per measure at a tempo like that. I tap my foot twice. On a fast jazz waltz, I tap my foot once per measure.
Yes I thought about this earlier. Really it's just another one of those "It just is" things. Trying to analyse what constitutes a beat and how long a note is in relation to beats etc is what I find odd.
So. Starting with a whole note you divide it into 2, 4 or 8. The length of a beat changes depending on what the time signature is. So the bottom number tells you what type of beat it is. The tempo tells you how often that beat occurs. The top number tells you how many of those beats fit in a bar.
1/4 note is not always one beat.