Tradition dies hard! And we all draw that line where we feel we want to!
I believe "Three under" is possible, and growing more popular, largly because of the availability of of our modern snap on nocks. With the Nirk nocks that we used in the 60s and 70s a bit of finger pinch from the split finger "Mediterranean draw" helped to secure the arrow tightly to the string. In my past personal experience, a little room between the string and bottom of the nock has resulted in a number of broken nocks and bad shots. And you'll still need it to hold the arrow against the riser if you'd like to try canting backward or shooting lying on your back etc.
Prior to plastic nocks, a shallow self nocked arrow was fairly common on this continent, and usually required a pinch draw, with the arrow held against the string between the thumb and index finger.
I'm not too well versed on the history of horn nocks and such overseas - what did the English longbows use?
Traditional is as Traditional does!