I've seen your potato harvest so I know what you're saying is correct, jal.
I suspect that the mulching trick is maybe typically utilized and necessary for gardeners like me in a small space that don't have abundance of extra soil to even minimally hill up with. But your point is well taken.
[Edited to add: also, my general impression -- James let's his potato plants sprawl which provides a certain amount of their own "mulch". If you need to "stake"/support the plants due to planting space issues, you may need to supply a certain amount of additional mulch to ensure adequate level of coverage.]
I think we've had several threads about the "tower" technique for growing potatoes reporting varying results. I believe one of the important points about that method is that you need to choose a long season potato variety. A short-season variety is robbed of above surface growth too much before the tubers form.
In my experience, a short tower method works for me in a new bed where I typically build a no-till raised bed over clay subsoil. Another point in favor is that in my humid area, it seems to be better not to start with a trench and below-ground level planting, although choosing a disease resistant variety helps.