Indexing
I'll have to search for one of the awesome technical explanations that have graced this site, but any machine will index in the absence of a brake or other mechanism that would otherwise hold the wash-tub stationary during agitation. Indexing is the sympathetic motion of the tub with respect to the stroke of the agitator.
It is precise, but it's equal-and-opposite, and you'll notice it's more pronounced with larger loads. My Westinghouse top-loader, in fact, would not index at all on lower water levels, but indexed brilliantly with a full load.
I totally agree about the agitators, and I can't figure why--when they had such a good thing going with the Westinghouse toploader ramped agitator--they'd ditch that and keep a suite of lousy-to-awful agitators around, none of which did that great of a job. You can't help but wonder if the ramped agitator would have rocked if remolded to fit the drive block of the Franklin mechanism.
Then again, with this design, I don't think WCI was out to rule the world through design--just through saturation.
And if it's any consolation, I think of doing laundry in this machine as "soaking the dirt away." Clothes still come out clean, oddly enough, even ones where I've blopped gravy on a shirt, or what have you. Still, a little rollover feels kind of good.
Do you have a vid of your dual-action Frigidaire washing? I'd love to have a look and see what that's like.