The point of looking first, as explained by my instructor, was to not freak out other drivers by signaling first. They might think you're going to suddenly pop out of the lane, spooking them to either speed up or slow down, or perhaps swirving, causing an accident that way. By looking first to make sure things are clear, you mitigate this risk. Of course, in heavy traffic this is still an issue; but heavy traffic typically means lower speeds as well so not necessarily as dangerous. That's the bit that comes with experience I suppose, learning when more attention is necessary.
My thought is that signaling before the full check gives the other driver a chance to make sure they're comfortable with and prepared for the change, but obviously you want to know they're there already.
I think the missing point in that SMOG acronym is general awareness. I don't know if they teach this, but I won't signal unless I'm already quite sure I'm lined up with a clear space I want to get into. But, once I'm aligned and think I'm good, I'll signal, double check mirrors, shoulder check, and then go. The only new info that gives is the shoulder check, and if you're paying attention a shoulder check should never surprise you.
If you need to change lanes within the next 30 seconds, and don't already have general knowledge of the destination lane's status, you've screwed up already. [1] It makes much more sense to consider checking after signaling if it's a double-check, not your first look at what's around you.