I can upload the favicon.ico file in Appearance -> Customize -> Site Identity just fine, but when I select the uploaded image to use as the Favicon the selection just hangs. My favicon is a 512×512, the file is an .ico file renamed from a .png file.
When I selected the same file to use as an embedded image on a regular post file (as a test to see if it was an issue with the file or media selection), it worked just fine.
I said the hell with it and just copied the .ico file to my document root. After all, it is just a favicon. Even then the favicon would not display in the browser tabs on FF, Chrome, or Edge. Oddly enough, the Favicon would appear on IE (ew!) I found a Stack Exchange post that had the same result but also got it to display when using Safari.
The Stack, Manually configured:
Generate Press 1.4
GP Premium 1.4.3
Chrome Version 60.0.3112.113 (Official Build) (64-bit)
MS/IE Version 11.608.15063.0CO
MS/Edge Version 40.15063.0.0
Firefox Version 55.0.3