Potatoes - how deep?

Potatoes have quite a root system and the tubers form along these roots, so I believe limiting depth could limit crop numbers and crop size due to congestion. If you had to grow shallow then I would give more room between plants. It may also mean that the plant is a bit less stable in wind. I've tried earthing up with additional compost or newspaper and grass clippings and both methods seemed to do the job equally well, I can't see why cardboard wouldn't work.
I'm a no dig gardener but I use a bulb planter to plant potatoes and a fork to harvest. Growing potatoes in no-dig is a bit of a compromise for me.