I understand your reasoning, but I think your logic is flawed. If Ladybird is GPLv3, then browsers will continue to use Chromium base which helps the Chrome monopoly. By making it BSD, it will help others adopt it.
Given the complexity of creating a new browser securely (or at all) then this suggestion is not good.
We already have projects that focus on smaller parts of a web browser (e.g a video player) which are free software. We should work on those and encourage their use over all browsers.
That is a massive undertaking that hasn't been done in a very long time. Modern browsers have either been around for 20 years or are forks. (Sometimes both)
We are taking about creating something from scratch. That can take 5-10 years to do.
The good news is that we have plenty of tools on our tool belt. Think browsers such as Mull and Librewolf plus extensions like ublock.