It still seems trivial to me. Parse all meta icon tags, prefer one that matches exact client resolution of current display (don't even have to download the icons - the sizes are defined as part of the meta tag), else use the largest-resolution one, else in desperate bid try site/favicon.ico, otherwise give up.

Really shouldn't be complicated enough to need a special service to handle "edge cases".

Another comment mentions web manifest - I guess try those first before meta tags, or whatever order the standard says to use. I mean, we're talking a web browser here, it's designed to do these kind of tasks.