SLJ

UK is the same, I've always tried to time things go we hit the Terminal just after 10AM regardless of what check in time they give on the set sail pass.
That way you get on board early and can start enjoying. Once you hear that little beep of them checking your pass on board its like a huge weight gets lifted, instant de-stress

Welcome to the message boards!
I usually check in when it becomes available only so that I don't forget to.  Luggage tags are often not available until 30-40 days out so that isn't a bad time to check in either.  

I've never heard of a benefit associated with when you check-in.  Of course, Royal's website has frequent issues so waiting to the last minute probably isn't a good idea.  Boarding times are meaningless for US departures.  You can always show up at the port starting around 10:30AM and be some of the first people on the ship.