Some people talk about tapping on 2 and 4 while playing. I have never seen any jazz piano legends, or bass players for that matter, tapping on 2 and 4 while in performance. Can you name any legends that do it?

Whatever the approach, they still have to subdivide the beat right? So I was taught to do the 2 and 4 in my head while tapping 1 and 3 on my foot.

Thus in this case, the subdivision wouldn't be visible to the audience...

It is common for the drummer to play the hi-hat [press the two cymbals together to make a "chick" sound ] on 2 and 4 and the rest of the band to listen for that.
Common but not a rule.

Any jazz pianist that can play will instinctively feel the 2 and the 4 while tapping on 1 and 3. How could it be otherwise?

exactly. And in my response, I was assuming solo piano. Obviously in a trio gig, the hi-hat already marks 2 and 4 so tapping that seems redundant. Why are you asking the question? Is there someone making a specific claim about the 'best' way to foot tap?

Many experienced players will tell you that the key to a swinging groove is "knowing where ONE is."

What exactly is meant by "tapping" in this context? It must be a stupid question, but I'm curious as to its purpose and why it matters whether it's done on the upbeat or downbeat.

Steven