If you get a case feeder, it's not so painful to run the brass through the press more than once.
For me, it would be unthinkable to push a new primer into a dirty pocket. All my guns and ammo are surgically clean. I'm being hyperbolic, but yeah, they're sparkly. My wife even makes fun of it because all my junk glitters. She comes into the garage and the lamps are reflecting off the brass and lighting up my eyes like a pirate brooding over a pile of glittering gold and she just laughs.
Jerry Miculek, who has reloaded and shot more than I ever will in my lifetime, has been reloading since the 1970's and says he never cleans primer pockets. He tumbles with the spent primers in. Back in the day, he dry tumbled, but switched to wet tumbling at some point. In one older video, he shows a used cement mixer for tumbling 5.56 brass. In a more recent video he really gave me the impression that he uses a Frankford Arsenal tumbler, even though he had the Hornady case cleaners displayed in front of it evidently because of his Hornady sponsorship. Obviously, guys like Miculek or Kinman (Hicock45) get large quantities of ammo from their sponsors. Their sponsors almost certainly don't provide their every desire for ammo. I imagine Miculek goes through large quantities of ammo for the few cartridges he uses for 3-gun, but he probably reloads for at least another dozen or two dozen cartridges that he probably only shoots in earthly quantities (no cement mixer needed). He also described switching from stainless steel pins to Southern Shine chips because the pins would get stuck in the spent primers and break his decapping pin. He says he's never cleaned a primer pocket since the 70's and doesn't see a reason to start. He can do what he likes.
I usually wash my spent cases first. I tumble them for 10 minutes in dish soap and stainless media in a STM Rebel 17 tumbler, separate them with a Frankford Arsenal media separator (the simple sieve that fits over a 5 gallon bucket), rinse them in hot water and shake and towel dry.
I lay them out or load them into loading blocks and spray them with Hornady One Shot case lube and let it dry for at least a minute. If they're rifle, I put Redding Imperial Wax on the necks with my fingers instead.
I load them in the case feeder.
Station 1 universal decaps them.
Station 2 resizes them, body for handgun, neck bushing for rifle
Station 3 resizes the neck (handgun only)
Station 4 expands the mouth (handgun only)
After this, they're loaded into the wet tumbler again with dish soap, stainless media and Lemishine.
I tumble for 30 minutes.
They come out with the primer pockets and inside the cases shiny.
I separate the media, rinse in hot water, and towel dry them. I blow them with an air compressor and let them air dry for at least a few hours.
Then I load them in the dry tumbler with corncob media that has a little bit of automotive protectant product in it (Meguiars Ultimate Wax which is actually not wax but a polymer type paint protectant and I choose it because its what I use on my cars)
They tumble for 30 minutes.
I separate the cases from the corncob (same Frankford sieve again)
Now they're ready to store in ziplock bags.
This is the point at which I would consider trimming cases or chamfer/deburr mouths. I will check cases after several loadings but I have never found brass that was even close to being too long. At most, I've only ever trimmed a half-dozen cases out of 500 because they were more than 2 thou longer than the other 494. I don't shoot anything high-pressure (the highest I go is 52,000 psi), so maybe my brass just doesn't stretch that much.
