What are the advantages of a monitor server for log shipping
You can monitor the process on the primary and secondaries, here's where a monitor comes in really useful though...

Let's say your log backups and copies are running just fine, no problems, but one of your secondaries goes down. You aren't monitoring the secondary and so are not aware of this. Your log shipping restore alerts are based off of the secondary server, so you are none the wiser (server being down then you are not getting restore alerts that things are out of date).

You notice a couple of days later, but by then it's too late and you have to restart log shipping from scratch.

Having a monitor server just helps to keep an eye on things and gives you a warning point not related to the servers involved in log shipping (think of it kind of like the witness server in mirroring, but without the automatic failover)