The time has come to consider chickens and eggs: rhythm and tone. Which comes first? In fairness I have to concede that it all depends.
For some people there is no problem giving rhythm priority. But for many others, myself included, awareness of tone can be so intense that it literally drowns out rhythm. In my case it was specifically awareness of piano tone. When at 15 I switched to organ there was no problem because the sound of the organ is so different, as is the coordination at the instrument.
My work with Tonal Refraction reveals that many others have similar perceptual imbalances. Some of these people are extremely gifted instrumentalists who are constantly being humiliated because they "can't count."
After many such experiences I had one lesson with Mieczyslaw Horszowski whose first reaction to my Schubert sonata was: "Your playing is quite mature. You do very interesting things with the rhythm. People are going to try to fix it. Don't let anybody fix it." The work of fixing it myself took a while but I felt marvelously supported every step of the way.
Giving priority to tone yields fascination with sound--a solid source of fascination with the piano and a reliable reason to not quit at age 15.