When I learned to tape bars in the 70s it was always from the inside, finishing at the bar end and sealing off with the plug. No sticky required. Tape was normally fabric. On my MAMIL rebirth some years ago I found that, along with other modern pointless flim flam like indexed gears, bar tape had got thicker and the accepted method was outside in, with the annoying sticky tape.
I tried wrapping modern fat bar tape the "right" way and I found that it doesn't sit as smoothly as fabric tape, and the edges get scuffed up if you do it the right way. So that's why the modern orthodoxy is to do things the wrong way, because the wrong way is right for fat tape on fat bars.
Usual disclaimer applies. I am an idiot and this may well be all cobblers.