I do realize that my preference matters nothing in the grand scheme of things. I just think "first touching" is less confusing for casual fans, is a better phrase to describe the outcome of the play, and I would prefer to not see it changed.
As for whether it is "illegal" seems to be a matter of semantics. Nowhere in the rules does it state that K cannot touch the kick first unless a fair catch signal has been given. 6-5-6(a) (though the exception clearly states that K may "catch, touch, muff, or bat" the kick if no R player is in a position to catch the ball). It just states an outcome of that action, much like the outcome of an incomplete catch is to return the ball to the previous spot, though I guess some in the world might call that the penalty for an incomplete pass. Again, I believe this is a matter of semantics, and I am solely familiar with the NFHS rulebook.
I do appreciate your pointing out my incorrect use of "recover." I had missed where it was defined and was using it in the colloquial sense. From now on I will do my best to use it in the proper sense and will speak in the sense of who will be next to have possession rather than who can recover.