I've been using that method for a long time,though I don't release a lot of cats these days.It works extremely well and is the only method I've used that calms the cat down and also covers all the other feet,and teeth.
The guy in the video was a little hesitant,putting the tote on.It's no good to just throw it on.You need to hold it down immediately.It doesn't take a lot of weight.I just put my knee on it.From that position,I can see all way around the rim of the container.I would also highly recommend not cutting a notch.There is no need for it and you could see that lead to a lot of fidgeting to rearrange the tote and the notch left room for the cat to get another front foot out and that could be bad.
The ones that I've done calmed down like you gave them a tranquilizer.Another thing worth mentioning,is that the cat's eyes adjust quickly to the dark and when you flip the tote off,they are dazed at first,I think from the sudden blast of sunlight in there eyes.That's also a plus.
Regarding having a tote,I carry a lot of gear in them so all I need to do is empty one and go.Personally,if I lived where I had to release a lot of cats,I'd figure a way to have one on hand.I can see exceptions like a trapper on foot but even a 4 wheeler could be organized to carry one.