I grow potatoes on a very small commercial scale, with hand tools, we plant our potatoes deep and do not hill as such. They do get a bit of extra soil pulled up round them preferably once, sometimes twice depending on how bad the weeds are, but that soil will be less than an inch in total.
Big bakers will get 3-4 inches when they hit flowering as they tend to push up out of the ground and go green. over the last 5 days we've dug 80lb of potatoes grown with no hilling at all (the weeds were nice to us) and we got 2 green potatoes out of all of that, hilling would not have been cost effective at all. These are of course first earlies (Solist) so the potatoes themselves are small. hilling pushes the production back and since we need the earliers possible potatoes to get the premium price and get traffic to the stand we do everything possible to get them out as early as possible including having them in a greenhouse!
I also help on the family farm which grows around 15-20 acres of potatoes, these are set and harvested by machine, so they are not planted as deep and the machine makes a mound over the seed piece, the reason is simply because the harvesting machine doesn't want to have to dig a foot down to get the potatoes so the seed piece is set about 1inch under the ground surface and a mount put over it. Once or twice the hiller will be put over the potatoes during the growing season. The main reason is to remove weeds but a secondary one is to reform the hills. since they are raised the soil tends to slump and get washed off a bit risking exposing the potatoes. I have never measured but I would guess that the hills end up around 6 inches higher than they started by the end of the season.
In my experience constant hilling is counter productive, we have a short season and blight is a when not an if, so anything that delays the harvest like burying all the food creating leaves is a dumb idea.