I think that's what the Pale Moon (https://www.palemoon.org/) folks were doing some time ago. I'm pretty sure they support most of the original firefox extensions without the signing etc.
I have been using Pale Moon x64 as my daily browser for years now. I have run into a few issues with extension compatibility, (ex: Greasemonkey has issues with versions newer than 1.15.1) but support is generally pretty good. I see it as a viable alternative to Firefox, but it could benefit from a little more mainstream support.