Not GP, but when I think about the negative consequences of BAT, I'm thinking about the user and society overall, not necessarily the website owner in specific.
Monetizing attention is dangerous, and I think we should be a lot more careful about when we do so, as opposed to monetizing attention being the default way we fund everything online. BAT is in many ways less harmful than existing advertising networks, but it's still trying to find a way to ethically commoditize otherwise private attention/focus on what we read/see, and I think that the omnipresent commoditization of that attention/focus across society is harmful regardless of whether or not it's invasive or collects PII and regardless of whether or not users get paid for selling something that we shouldn't encourage them to sell. I think that this has an effect on how humans process the world, I think it has an effect on how much energy we're willing to devote to different tasks. I think it has an effect on attention spans, and on what types of content get made, and the way that we spread memes/culture, and how we interact with each other. I think it has an effect on market efficiency and on what products succeed. I'm not going to oversell modern advertising as some kind of giant monster that's responsible for all problems, but I think its effects are likely more negative than positive at this point and that we can build better systems that don't optimize for keeping people hooked on consuming content endlessly just so we can redirect some of that attention to a product.
As a website owner, the social stuff still applies to me, I may not want my stuff commoditized at all. But I also recognize that users have the right to modify code running on their computer, including for the purposes of inserting their own ads, so if it's happening with the user's permission I can't really get mad at the user. In many ways I'm the least impacted person in this situation. However, that doesn't mean that I think Brave's system is good for the user or for society, and I'm not going to encourage people to use it.
My feeling is that Brave is trying to reform a system that I would like to see destroyed.
If Brave users opt into Brave Rewards for private user ads in push notifications (which, contra Butterick, do not belong to any page they might be near or above; they belong to the user's inventory, same as new tabs and unrelated windows of all kinds), we still wouldn't put ads in pages without both publisher and extra user consent (too many users still wouldn't want in-page ads, even if opted into user push notification ads).
HN is full of made up nonsense about Brave, in spite of all the hackers here who can verify our open source, network behavior, etc. etc. This site has seen better days.
However, I also had negative opinions of it like many people here before I really dug into it. I think your marketing really needs some work. I don't exactly know what it is - it might not even be your fault. The negative view of crypto many have has been associated with it. I would remove all mentions of crypto from your website. If people really want to know how the tokens work, they can go into the documentation. Having the word crypto on your landing page does you no good.
Talk is cheap, especially stories that don't pass any kind of smell test: we would not take our life into our hands by collecting any user data, when it's easy to discover that for real hackers.
https://brave.com/data covers our data policies for baseline and optional stuff.