I usually ridge the potatoes, but there have been years when for one reason or another it hasn't been done, or it's only been done once. What I have found is that....it depends on the potato variety
Some varieties grow much closer to the surface than others and these were the ones where I would lose a good half of the crop to greening, which is indicative of toxins in the potato. With some varieties though hardly any potatoes were near the surface, so I only lost a few. Which varieties were which?....I haven't a clue
I have tried growing under black polythene to keep out the light but found some light got through, so again the top tubers were greened.
I don't think it makes any difference how deeply you plant the tubers initially, because they start forming new ones just below where their stem comes to the surface of the soil, rather than around the original tuber. I do think that earthing up can make a difference to overall yield for two reasons: one is that if your soil is nicely fertile then the tubers themselves have good access to this fertility with plenty of fresh soil piled around them; and when they are earthed up there is plenty of soil to hold rainwater close to the tubers to help them swell.
I intend to earth up my potatoes this year but with the endless wet in this part of Scotland I must admit I haven't done it yet. Maybe I will just use a thick mulch as you say FiB.