Progressives make ammo faster. All progressives suffer some level of shellplate deflection, this effects primarily OAL, but can mess with sizing (esp. headspace of bottlenecks) and run-out. The variances deflection cause can be somewhat reduced case sorting by headstamp, and lubing cases.
My old Lee Challenger absolutely deflects visibly when sizing rifle cases, the old Rock Chucker I learned on surely did, but not visibly.
Now, what's it matter? Well loading for auto pistols if there is enough variance in OAL or how far down my brass gets sized I end up with bullets jamming the lands and/or failures to go fully into battery, one's obnoxious, the other could be dangerous, just things you have to check for and tune to acceptable. If I shot bullseye competition or benchrest pistol I would be more concerned as the variances would equal sacrificed precision.
For the single stage, press deflection has caused me an occasional issue of not bumping the shoulder back far enough, and surely some inconsistency when it does. My rounds probably also have some run-out, less than my eyes measure. If there's some wild difference in brass I can have some seating issues from the difference in neck tension. That said if your loads are not refined to the point that you consider +/- 1/4" in group size at 100yds a substantial change it's probably not worth worrying over as long as the headspace is swinging dangerously. Still if you have "better" equipment for your end goal use it, can't hurt.