It's the same deal with a nonphysical attack. How is 8 letters username + 8 letters password harder or easier to crack than a 16 letters password? Even provided that both username and password WERE secret, which they usually are not, you don't gain security by splitting up a X-bit key into two keys Y and Z that have together a length of len(X). It is the same attack complexity. How are the two tokens "username" and "password" harder or easier to brute force than the one token "usernamepassword"?
The point is that the user name, the part that makes up the identity of the authorization process, is NOT part of the authentication. Your username identifies you. It does nothing else. It's not even secret, mostly because it CANNOT be under nearly all circumstances. As soon as other users have to interact with you in some way, they need some token to address you by. And while it is possible to come up with elaborate schemes how to keep that username secret, they all have some flaw at some point.
The username is also not something the server can use to verify anything because it is your claim, your proposition, rather than something it can verify. You claim that you are user abcd. That's basically what you say when you log in. You make a claim. That by itself does not add anything to security. It is just something you claim to be. You might have noticed that when you log in, your username is also not hidden in the input mask, unlike your password. Because it simply is not a security secret. It is just a claim. You claim to be that user.
To verify that this claim is genuine the server will want something from you that allows him to authenticate this claim. Your password. If you want to make that password longer, go ahead. Yes, that would actually increase security against brute force attacks (not against keylogging, but against brute force attempts). But adding further passwords does not add any security. Either I can brute force them all, in which case there is no gain from having more instead of longer passwords, or I can keylog them all, in which case it matters little whether I have to record one or seven passwords.