In general I think extensions with functionality like this that require unfettered access reading and modifying every single page you visit are a huge security concern so having it be part of the browser itself makes sense. Same logic applies to ad- and tracker-blocking.

This touches on the topic of who writes it. Yes, it is nicer to have it written by a big player like Brave than by some guy from the internet.

But why did Brave have to put it into their browser and did not publish it as a plugin?

> But why did Brave have to put it into their browser and did not publish it as a plugin?

I don't know if they do that in this case, but one could assume having access to non-public internal APIs might improve filtering capabilities/performance.

For example if brave was to implement manifest v3, it wouldn't impact their built-in ad/cookie blocking features.

This isn't a plugin. The cookie blocking is just an extra filterlist that's built to be compatible with uBlock Origin and Brave Shields, and has been available for both for a while. The innovation is simply the browser proactively using a prompt to ask the user if they want to subscribe to the list.