Agreed in principle. It's my primary browser and it seems to me that it's already in good shape (technically, and feature-wise). And the project is not starting from scratch.
So if the financial incentives aren't there yet, and the only remaining value that Firefox provides is privacy and user freedom (along with good but not perfect performance), I'd imagine the FSF could be interested in managing something like this. And can maybe start with part-time volunteers.
This makes it even harder from my p-o-v. Most contributors want to create something new and not maintain old legacy, grown over a few decades. Diving deep enough is work and might happen once in a while for a bug which is a pain for somebody curious ... but tough sell.
So if the financial incentives aren't there yet, and the only remaining value that Firefox provides is privacy and user freedom (along with good but not perfect performance), I'd imagine the FSF could be interested in managing something like this. And can maybe start with part-time volunteers.