I'm on macOS 10.13 High Sierra with Safari 11.
I noticed that whenever I close an re-open Safari, it keeps reloading all of the favicons for every bookmark as if I freshly set it up. When I made the upgrade to High Sierra I reinstalled my MacBook from scratch. Since then the issue with the bookmark icons surfaced. The new tracking protections under privacy settings don't seem to cause the issue, since icons reload even when I turn them off.
I tried deleting Safari .plist files in ~/Library/Preferences, deleting the ~/Library/Safari directory but to no avail.
Although it's just a minor issue it's annoying and could burn a lot of data when I'm on the go and use my iPhone as mobile hotspot (from what I understand Safari loads the .png web app icons instead of the favicon.ico files which should be considerably larger in file size).
Best Answer
I realise a "me too" is not helpful, but I wanted to keep the discussion alive. This is the first post I have found on this subject after several attempts. So, good to know I am not alone.
Unfortunately, the answer from Geek is only a work-around. I work a lot on my Mac with a data plan and I like the favourites tiles / icons on my new tabs.
However, this does not happen on all Macs. I have a much-older MacBook air where this does not happen in High Sierra, but on a more recent MacBook Air I do see this every time.
The main difference between these machines, is that the one that has this issue is configured as a work Domain account, or in other words, as a Mobile device.