I think the question most would ask is what does Brave offer? Outside of tech, I don't think most people are willing to experiment with new(ish) software unless there's a very compelling advantage (and for most, I don't think BAT is a feature)
It wouldn't be created and run by Brendan Eich who was run out of Mozilla for the crime of (privately) voting the wrong way on a ballot initiative. That was and continues to be a bad look for Mozilla.
Profit motive does not go away in a "non-profit" (FYI, Firefox is produced by the Mozilla Corporation, which is the for-profit subsidiary of the Mozilla Foundation; top salary last seen [2017] was $2.3M+). Mozilla depends for its profits (to pay such salaries and bonuses) mainly on the Google search deal.
In my opinion, this conflict of interest between users and Mozilla's search revenue share held back tracking protection in Firefox over the years. We (I was there, this is all in public bugs and news now) rejected third-party cookie blocking three times.
Meanwhile Brave has a transparent rate card, where we pay the user 70% of the gross revenue for user-private ads, and 15% for publisher ads (not yet deployed; the publisher makes 70% and we take same as the user). So we get <= what users get, and we will fail if our users don't like the private/anonymous ads+donation model enough to opt in at sufficient scale that we can cover our costs.