And here's why.

If root has a password, and you've not disabled remote root logins, and you haven't disabled any crashy/buggy services that run as root and which could be compromised to get a shell, then an attacker doesn't even have to think about the username and can move swiftly on to the password part of things.

If you have a sensible username, then the attacker has to go through the hoops of finding a username to compromise, hoping it's in /etc/sudoers, and then hoping also that he can crack the password.

There's no such thing as total security, obviously (well, there is, but it involves your computer being in a locked, booby-trapped box at the bottom of the Marianas trench with a sign saying "Beware of the tiger" on the door[0]) but it seems silly to me to not use an obvious security feature like this.

Other benefits of using the sudo approach include not inadvertently still being root when you're rather not be (people like me who "sudo su" deserve everything they get) and also only having the one password to remember so, therefore you can make it much stronger.

It's horses for courses, naturally. Some people really find the sudo method extremely intrusive. Personally, I like it.

You can restrict the activities of users in many ways.

You could give yourself, say, the ability to change other users' passwords but not to run dpkg, for example.

Read the man page and documentation. The syntax of /etc/sudoers takes some getting used to, so be warned :-)