I mean, you might then argue that the Echo (and, for that matter, Amazon generally) was insufficiently surreptitious about it. If Brave can be more difficult to distinguish, it will also be more difficult to ban.

No, you might then argue that. :) Look how Uber’s behavior with paging and canceling Lyft rides during their poaching days came back to bite them in the ass. And I’m sure if Amazon’s small army of lawyers felt they had a leg to stand on with the UserAgent obfuscation route, they would do it.