Does it not add a step/process to then remove the sized/deprimed case and then take it to my hand primer. Then put that case back in the press?
Yes, it would. Except my sized, deprimed, and mouth expanded cases make a pass though the tumbler before being primed.
I resize and prep cases shortly after shooting. I do not let unprepared cases accumulate. These batches are small, relatively, and I cruise through a days shooting in 5-10 minutes/100 handgun cases. Rifle takes a bit longer due to lubricating and trimming. But, after tumbling rifle cases, I am not handling gooey, slick cases either. Lots of this work can be done while watching the tube or grooving to my favorite tunes. Ah, multitasking!
I store the prepped cases away. When I need, or decide to load a particular cartridge, I prime the cases by hand then load them on the progressive. Most of my process interruptions on a progressive press come in the resizing die area and the priming system. By resizing at another time and priming by hand, I eliminate the downtime caused in those areas.
All three of my progressive presses, one Hornady and two Dillons, have had the priming system removed. My progressive press priming systems are not reliable or robust enough for my liking. Perfect would be about right, or the ability to inspect the seated primer before dropping powder would work.
I hate rework worse than trimming cases.
But I do have some idiosyncrasies. Your loading preferences may or will differ.