the argument b/t Li and Chinese Tennis Association was not about prize money (I heard that a lot on ESPN but they were wrong on this). Chinese tennis players like Li Na, Zheng Jie or Peng they were recruited by the association at young ages, the association spent about US$ 0.5M~1M on each player each year, that includes everything from apparels, equipments, traveling, to coaching, physio and treatments etc. Li also received monthly stipend from the government. When Li Na finally broke free from the association, she knew it's not easy to be on tour "alone", she had prepared for the worst - her savings account could quickly drop to zero. Li mentioned in the interviews and also in her bio, she needed to find sponsors, and "small" things like booking a hotel room and airline tickets became her job. In the past all these tings were taken care of by the association, all she had to do is to bring her racket and play a match on court. The total of 65% cut of prize money taken by the association may sound a lot, but in reality, it's really nothing when compared the investment spent on those players, and most of them never won any significant prize money on tour.
You are right about Li choosing her own coach. The association had some very rigid rules on who can coach whom, and they also had very tight control on player's schedule. They would force the players to withdraw from tournaments or grand slams to play at national games or Asian games if there are some conflicting schedules. And these are the main reasons Li Na left the association.