Early on in a connection, congestion window is much more limiting than bandwidth delay product. Do you really want to spend that limited bandwidth on your favicon that you might have already sent to the user before, maybe even in the same browsing session?

It's way better to put it as a separate image, maybe their browser will delay loading it because they're mostly useless. But, you can actually make a favicon useful! If you serve http-strict-transport-security headers with includeSubdomains from your top level domain and you serve your favicon from there, you can push browsers to load them. Ex: your website at www.example.org loads https://example.org/f as its favicon with content expiration about the same as HSTS expiration, and you've now set or refreshed that.