I do not know the full details on how the current process works. But I believe it is a technical issue.
The rewards you receive are in the form of vBAT, a virtual asset representing BAT.
If you link your browser to an account in Uphold or Gemini, the balance of vBAT you earn is somehow (don’t ask me how) communicated to them. They will convert vBAT into BAT internally (as part of their agreement). No blockchain transactions occur. Thus, this can be done seamless.
On the other end, if you transfer BAT to a non-custodial wallet, like Brave Wallet, the transaction occurs in the Ethereum blockchain. Fees are charged.
As most of you know, Ethereum fees are not cheap. For monthly rewards worth 5 USD you would likely pay 50 USD of fees.
This is my understanding. I do not have the whole picture, but that’s how I interprete the process.