primer pockets should be cleaned also.
Seen too much evidence that this is false to place any stock in the value of cleaning primer pockets... Banging around for hours on end in a tumbler just dings and hardens you necks.
...and you're kidding, right? I'll believe it when I see actual scientific testing that supports it. The forces involved are so miniscule that the brass isn't even deflected. No deflection, no work hardening.
This is from Vamint Al's Reloading page, a guy who know a little bit about the subject.... But hey, you know better right...

NECK MOUTH.... On the left is a brand new 243 Win brass and you can see the rolled over edges of the mouth do to the hammering that occurs in the polishing process. Also the hammered area is work hardened and locally is no longer in the annealed state. If you have ever noticed a tiny ring of gilding metal scraped off when you seat a bullet, it is this hard rolled over ring of brass that does the scraping. Even after inside and outside chamfering, there is still a burr left at the edge of the cut surface.
On the right is one of my 23/40 brass cases after the neck has been trimmed square and fired a number of times. I gave it about 30 revolutions in the Steel Wool Spinner to show how smooth the neck mouth is. With the smooth annealed neck and no rolled over burr, bullets seat very smoothly without scraping gilding metal of the bullet.
.... Smooth and uniform case mouths are very important in producing accurate reloads. Therefore, I don't polish my carefully prepared brass in a tumbler. During polishing, the case mouths are hammered against the other cases in the tumbler. The hammering rolls over a small lip or burr on the ID and OD of each case mouth. This peening process also locally work hardens the brass. These tiny rolled-over rings of brass at the case mouths are harder than the rest of the annealed neck. These rings and tiny peen marks are very obvious on new brass. If you look at your nice shiny cleaned cases out of the tumbler, you will see the battered case mouths!
http://www.varmintal.com/arelo.htm