Say I was in a web chatroom using SSL and someone posted a link to a piracy site. I right click and want to share it. Previously only the chatroom administrator could have known that my IP saw that link. But now, my ISP or anyone sniffing packets on the network would be able to see that I inadvertently accessed the URL. Regardless of whether or not I did anything else on the website, I could possibly get into trouble for simply requesting content from it.

Maybe instead it's a link to a site that sells abortion pills and I'm a pregnant woman under a government that forbids them. I share it with someone else but don't access it myself. Maybe I have a miscarriage and the government suspects it's actually an abortion. They get a warrant for ISP records and now there's proof I accessed a site selling abortion pills despite never actually going to the website.

Or maybe it's a link to an IP stealer. Someone asks you to share it with someone else. You don't click the link but they still grab your IP anyway when you go to share it.

I can think of numerous other examples of how a compromising URL could expose your activities even if you didn't actually click on the link. I don't really see a need for downloading a preview favicon. It just exposes you for no reason and could provide just another possible attack vector