Like many reloading procedures, actually quantifying a small potential difference is difficult if not impossible. For example, I uniform my primer pockets only once when I first prep factory brass, even Lapua. But some of my competitors uniform their primer pockets every time. On the other hand, I anneal every time and they don't. Differences? I think it comes down to that you "think" will help. I've done enough testing to be convinced that you'll wear out your barrel before you can truly find a measurable difference in a single procedure which is expected to produce only a tiny improvement, if it does so at all.
Chances are small improvements all add up, which is why most of us do a lot of prep work and take great care trying to make the best reloads. But deciding exactly how much a single procedure helps is hard to say.
I do know this. I hate handling individual pieces more than necessary and that's why I use a Lock N Load progressive with a DIY case feeder for both plinking ammo and competition ammo. I shoot single shot rifles and keep my brass clean at the range, so my competition routine is lube then set up my press to batch feed, deprime, bushing neck size, body size, and finally insert a special sizing mandrel to uniform the neck, all in one pass through the press. Then I trim, chamfer, wet SS clean, dry, and anneal. Next I batch feed the brass through the press where I insert the sizing mandrel again as I prime. Next I weigh each charge to .02gr, fill the cartridges and finally use the press as a single stage to seat the bullets. This makes ammo good enough to win my fair share of local 600 yd F-class and BR matches.
That involves plenty of individual handling, but not nearly as much as a single stage press. For plinking, the progressive really shines because once the brass is clean, I can prime, charge cases, and seat bullets in one pass by only handling the bullets. And if the world collapses and you need a lot of rough ammo in a hurry, you can eliminate cleaning and do the whole process in one pass.
Of course I carefully measure my finished competition ammo and find that it is well within accepted tolerances for seating depth, run-out, etc. Plus it seems to work well. The progressive press takes out just enough of the PITA factor so that I don't mind loading ammo.
For example, this week I did some fine tuning of seating depth and loaded a batch of competition ammo based on that testing; i.e. I made two medium sized batches in a few days without dreading the job. My shooting buddy who uses a single stage press has been looking at a pile of cases for over a month and just can bring himself to trudge through the tedious reloading process. Tomorrow I'm going out of town for a match but he's staying home since he couldn't bring himself to get ready using his single stage.
Of course, your mileage may vary. But if you ask me, a progressive press is plenty accurate and makes my life easier. I'm going to stick with my progressive until I get so crazy that I start weight sorting my primers.