Yes, missing favicons do affect performance.
As you probably already know, adding a favorite icon to your website is a great way to add subtle branding to your website. It’s an easy, one-time update to your website that you never need to think about once it’s done.
Lets say you don’t care about the favicon or don’t have a logo to use as a favicon. Since each browser looks for a “favicon.ico” file when no favicon is assigned, your server may throw off 404 errors on every site visit. What a bunch of wasted bandwidth and server strain!
The solution is to use a blank favicon file. It’s tiny in size, prevents the useless 404 error, and decreases load on the server.