Nikon D500 = Best Nikon's Sport Camera
With 20.7 Mp, 10 FPS, and crop factor x1.5, I can tell it's dream camera for sport photographers whom holding two cameras in the field.
First, I will tell you why this camera is good for sport photography. With our Nikkor 800mm F/5.6, it will give you on that camera not 800mm F/5.6, but it will give you 1200mm F/5.6. YES!! Can you image how 1200mm looks like now?
I totally understand what you want to have. But, why Nikon D500's score is less than Nikon D7200?
Second, Remember this: YOU WILL NEVER GET A PERFECT CAMERA FOR EVERYTHING.
The company's strategy decided this camera Nikon D500 with high FPS (10 FPS) with lower MP (20.7~21MP). Nikon D7200 higher MP (24MP) but lower FPS. Don't let this effect your ways of buying or deciding which camera to buy. There is no difference between 21 and 24 in general as soon as you are getting the right angel and shooting settings.
Finally, You are who you are. you are the one who decide to which one to buy. I tried Both Nikon D500 and Nikon D7200 and It's just a tool and almost same feelings with holding. If you want sport camera without buying Nikon D5 or Nikon D4s, get Nikon D500 it's the best DX sport camera which will support you in all ways capturing the moments. Don't for get numbers one point AF, it's faster than Nikon D7200. Don't buy this camera for lans