Yep, thats what we do too. We just pour some water over the griddle while its still very hot and scrub it with this steel cloth thingee with a towel over it. Small hard rubs. Then we wipe it down and wipe on some vegetable oil. Every month or so we use the grill cleaner, but no more than once every 3 weeks. It scrapes off all that good non-stick seasoning.
A Japanese place I have been to uses water with a stainless steel scrubbie for a very fast clean up. They hold the scrubbie with a wet towel and scrub off the grill. Not sure if they put anything in the water. I have never tried it but have thought I might.
I prefer to use grill screens with oil rather than grill bricks. I think they get the grill cleaner and they don't make you stink like those nasty grill bricks! Either way just takes lots of muscles.