We’re working on an experimental build of Brave which may reduce the number of CAPTCHAs encountered as you browse the Web. I hope to have a link available shortly for those who would like to help test, and are aware of (and okay with) the brittle nature of a preview build. Fortunately, these builds can be installed on the same system as a Stable/Release build of Brave, so there is no need to overwrite your main instance of Brave.
More information to share soon! Thank you all again for helping us determine the size and scope of this issue, and for your incredible patience while we work to improve the experience.