Someone needs to buy the BAT tokens on Coinbase. Who does that? There doesn’t seem to be an obvious reason for anyone to hold this token.
Is it Brave themselves buying the tokens or paying a market maker? That would complete the loop you describe where the token is simply a way for them to pay semi-anonymously.
The loop is that advertisers acquire BAT (typically by purchasing it for cash from an exchange like Coinbase). That BAT is then distributed to people who view the advertisements, who then sell it back to the advertisers for cash.
Brave does not buy the token or pay any market maker, it's a simple cycle between advertisers and viewers.
Is it Brave themselves buying the tokens or paying a market maker? That would complete the loop you describe where the token is simply a way for them to pay semi-anonymously.