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.