Matt, John F, & piaa_ump:
You guys are all more experienced umps than I, and you seem agreed that it's not necessary to call time to clean the plate.
Is the reason based on a pre-disposition to keep the ball live and avoid unnecessary stoppages, signals, and calls? Is it that with more experience, you have confidence to keep a lighter hand on the reins? Or is there something else going on?
I know I can respond appropriately to a situation in which a coach attempts what PitchingFan suggested (in jest, I think), and I can do so in a manner that discourages similar shenanigans by anyone who remains in the game after such a breach of decorum. But throwing my hands in the air for a fraction of a second before cleaning the plate seems like a cheap insurance policy. Otherwise, any action that occurs while I'm brushing is likely to lead to an argument.
What am I missing?
Seriously, I'm not trying to argue. Trying to learn.
The part I've highlighted in bold is pretty much it. Leaving the ball live as much as possible allows both teams to play their game as much as possible. At lower levels, you can't necessarily do this--I've never seen anyone over the age of 18 try to steal home with the pitcher holding the ball during relaxed action.