I don't understand the argument that you're making here. If she is suffering from depression and wants to withdraw from the press commitments but not the tennis, this puts her at an advantage over other players.

If all players who wanted to avoid press engagement simply said they were too depressed to attend then there would be zero press engagement. Most athletes aren't naturally extroverted, the intense training for single sports probably favouring introverts.

With zero press engagement, there would be a lack of funding for the sport and sponsorship would dwindle. If tennis players want to continue to enjoy the high pay per game they must adhere to further rules around sponsorship. If they don't want to do this - for whatever reason, they should be allowed to take time away from the sport. There may be a propensity for black atheletes to be more prone to depression. This might also be true of gay athletes, shy athletes or those from a different socioeconomic class. You cannot give special treatment to one group of people without opening up the floodgates for special treatment for any self identified grouping.

So far she has offered to play without doing press. The tennis world has said no. She has said she won't play. The tennis world said fine. She's not playing. I can't see the problem here as the communication has been clear. I hope she gets better and I'm sure she can afford some decent therapy and get herself media training to reduce her anxiety. Then she'll be back and we can all enjoy watching her play again.

UPDATE: I turned this comment into a story of its own. https://medium.com/lucid-nightmare/naomi-osaka-and-the-ongoing-infantilisation-of-mental-health-a4978ff14e58