In my previous home, I had a top of the line (at the time) top loading HE Maytag with the squat agitator. There was very little to no turnover of the items being washed, when viewed through the window in the lid. As georgect mentioned below, you can find numerous YouTube videos documenting the problem. This resulted in items not being cleaned well and additional wear and tear on clothes and linens. I'd let it fill up and get started at which point I'd pause the machine, unlock the lid and dump in a pail or two of water, just to get better agitation. So much for HE and saving water.
I recall reading that some were resorting to purchasing commercial top loaders to get around the problem. Apparently, the water regulations weren't (or aren't) as strict as with residential machines. And they cost way more too.
Some current model residential machines have a "Deep Fill" button that adds additional water - perhaps a resolution to the problem? Don't know, since in my current home, I went with a front loader because of space constraints requiring a stacked washer and dryer. I am very happy with the front loader. It cleans very well while still saving on water. I'd never go back to a top loader, even if I had the space.
Q