The problem with that is that different people viewing the same URL (/profile.php) gets a different resource. What happens if someone gives a link to his profile.php over IM or something, expecting it to show his own profile? The URL the user is shown in the address bar should represent the current resource being viewed.
A better solution could be to replace links to profile.php with direct links to the real profile URL, and just kill that profile.php redirection.
see a different resource? For a web app like FB I don't think this avoidable. All data served is dependent on who you are when you are logged in.
For another example of how to handle this better, see twitter:
twitter.com - the user's feed, content differs for each user
twitter.com/username - the user's public url, for sharing, a proper URI which everyone can use
twitter.com/settings/profile - the user's private profile, content differs for each user
I agree they shouldn't need that redirection with no id supplied and I suspect it's just a legacy of the original way of showing profiles (profile.php?id=n), they could just redirect it to root instead (shows the same as profile.php it seems) to avoid leaking state.
A better solution could be to replace links to profile.php with direct links to the real profile URL, and just kill that profile.php redirection.