Its a nice idea, but at first why should you scan the browsing history, bookmarks and so on?
The chance, that there would be a virus is very low, because how should it be executed?
And the secend thing is i personally think its a waste of resources, because the most people have already an antivirus running and a second would just slow down the pc.
And as stated in the other comment: it has to be an open source antivirus otherwise its totally against the idea of Brave.

P.s. if you want more security, then just use Linux. :)
Its a lot more secure and private and there are many nice distributions out there, with different features, different look.
So there should be something for everybody. :)
I recently installed for example Elementary OS.
Its worth a look.
And if you need windows programms, you can usw wine. :)