I think you’re right that the former license can’t be taken away from other instances.
Some projects chooses a license specifically to stop people taking code without sharing code back upon redistribution via copyleft (ShareAlike). Getting around that by changing the license defeats the purpose (projecting users software freedom).
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.