IMO...
I looked at the Taylor video and my reaction was, why would I do that? I see no advantage to it, only disadvantage.
I've been stringing guitars for more years than I care to mention and there can be NO issues with stringing the guitar with the string and, after pulling them up to pitch, clipping off the excess. Clipping it first can cause unraveling as noted on some strings AND a possibility of cutting it to the wrong length. That's "operator error?" Sure, but why not eliminate the possibility completely?
The string winds DOWN toward the peg head to ensure decent break across the nut. Also, the minimum amount of string on the peg needed to provide holding and downbearing on the nut provides better tuning stability. The more turns of string on the peg, the more time it takes for tuning to settle.
Single string or all at once? Whatever you want to do. It doesn't matter to the instrument OTHER than the fact that if you remove them all at once, tuning stability will take a bit longer as the neck totally relaxes and then has to curve again when the strings are brought up to pitch. If you are in a hurry for stability, do it one at a time. If you can wait an hour before it has to play on stage or wherever, then all at once will be fine.
Again, the above is MY OPINION based on a lot of years of doing this on steel and nylon stringed guitars. But it is just an opinion.
