I like to deprime my brass before wet tumbling.
An open primer hole allows the primer pocket itself to be cleaned (when using stainless steel pins) and lets the water flow through and out easier and completely. Shells dry faster too.
Another reason to deprime is to make sure I don't accidentally reseat a spent primer during reloading on my Dillion 550. Don't laugh. It has happened to me. Somehow, a spent primer is pushed out with the depriming pin in the sizing die, but sticks to the pin and gets pulled back into the primer pocket and I then load the shell with a dead primer. This cannot happen if the brass is deprimed.
I usually sit at my bench and poke out the spent primers using an old Lee press and a Lee Universal Decapping Die.
The problem is: DEPRIMING IS BORING.
So I've found I can sit in my living room and watch a mindless movie while I mindlessly deprime my brass.
To do this, I like using the Frankford Arsenal Hand Depriming tool.
Last night depriming a couple hundred 9mm, and a few random .380acp and .40 S&W went surprisingly fast, considering I would have been sitting in the same chair just watching a dumb movie.
One other advantage of depriming: I can catch errant caliber shells that got though the initial sorting.