Oh, this is for putting an icon next to search results? Yeah, that changes the calculus considerably. I thought this was about showing the favicon in the browser for a site the user visits (per the issue title).
In that case, yeah, I don't think the icons are necessary to show at all...
Even if you wanted to implement this, the logic of the service could be directly embedded in the browser as an extension or similar. There’s no reason to depend on a network service for this functionality.
I feel like the only user benefit is to see the favicons of sites you are familiar with, so caching those locally after you visit sites is probably good enough.
In that case, yeah, I don't think the icons are necessary to show at all...