Would you mind sharing why you want progress toward eliminating favicons? Do you think there is some other replacement, or that nothing at all should be used?
For me, I know having small icons helps me scroll through my bookmarks and identify resources I want to reference. Even if the shape of the icon is poor at a small resolution, I think my brain picks up on the color association. So just for the sake of finding things in my bookmarks, I can't imagine getting rid of favicons.
I hate them because they are requested automatically, rather than because the developer declared them. They clog my web server logs when I build microservices and in development they double up every page request. I still remember when they first started happening and they just broke the mental model that web pages were built on. From my software aesthetic perspective they disgust me.
Having an icon for bookmarks and tabs is totally, 100% great - don't get me wrong. but they should be off by default.