This has been discussed before. According to Brave, if we want to see Binance or any other exchanges/wallets for use, then we need to write those places. Brave is constantly looking to add partners but that’s a business deal that has to be made. Binance has to want to work with Brave and allow Users to link their accounts to them.
To quote Brendan Eich:
The process in having a business relationship with exchanges is more difficult than Users may realize. There are a lot of fees and other arrangements that need to be set up to happen.
That said, we are in talks with multiple and hoping to reach new deals to expand offerings. In fact, we can’t give details, but we have a major deal we’re hoping to reach soon that would make Users very happy. We are also always reaching out and trying to do business with other companies, but it takes time.
So all I can tell you is for you and other Users to start reaching out to support for those companies. Tell them you use Brave and would like to see them partner with it so you can receive your BAT there. If enough people do that, they may reach out and deals can be made, which would allow you to link with them.