I usually tumble mine with the spent primers still in place, then pop and clean the pockets/flash holes good. I'm not convinced this doesn't help - albeit a very little. I sort my brass by lengths after the spent primers are removed, then clean primers pockets, then debur/chamfer case necks, then neck size - charge - and seat bullets again. I did get a primer pocket tool in the early going, but I have yet to use the darn thing. Always been afraid of cutting the pockets too deep with it. I use a little brush now from RCBS (one for small rifle, another for large rifle pockets) to clean. Before that, I just scratched out the worst of it with a bent paper clip.
I went the neck sizing route to eliminate case lube (plus reduce case wear & improve accuracy), so I'm always looking for ways to make the process more efficient. Maybe I'll have to rethink cleaning these pockets so thoroughly each and every time. ?