There are two main reasons why this is not (yet) possible.
The first one is due to regulations. In order to distribute rewards directly to the users wallets, Brave would be forced to the KYC and store user data. This is complex, it would require compliance with several regulations, licenses and technically the reinforcement of data storage capacity, security, etc.
The second reason is due to the fact that BAT is a token in the Ethereum network. Transferring BAT to the Brave wallet would have to be done on-chain. Currently it is done off-chain with the partnership of Uphold and Gemini. Transfers on-chain in Ethereum are expensive. In most cases the value of the fees would be higher than the value of rewards.
The good news is that Brave is aware of these constraints and thinking about possible alternatives. There are rumours that some news may come in the near future.