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Brave does follow this patreon style model. There's a section in the Brave Rewards panel that mentions "Auto-contribute" which does what your describing.

You can also easily enable and disable Brave Ads while still contributing (though you'd need to fund your browser wallet)

Doesn't every single website have to opt in for this to receive any payment?

This is really hard to do because it involves a myriad of ad networks and payment systems. Others have tried to solve it but maybe Brave can? Dunno.

That'd be a really nice feature