Jim while I agree with on point two, you are mistaken about other sports not having licenses.

Many states license the ownership of handguns, this is in effect a license on the sport of shooting (I saw an interesting story on TV where a British woman training for the Olympics was going to have to leave the country because they had outlawed the gun she used to compete). And of course we can debate about whether hunting is a sport, but there are hunting and fishing licenses (while their primary purpose is revenue generation they can be revoked or declined for "bad conduct").

And then we can address the issue of school athletes. Many Public High Schools have created student athlete rules that govern players conduct (both on and off the field) and effectively operate as a licensing system. Although they can not prevent people from participating in the sport outside of the school, for many sports there simply are no other ways to particpate. (While baseball has little league where does a 14 year old pole vaulter compete other than through the School.)

That being said you of course know what I think of those licenses.