I find it best to alternate between the two. The one shoulder method has the advantage of leaving a hand free for short scrambling sections and it's easier to lift the bike up and put it back down. I find the one you show a good alternative, particularly when it's an easy carry with no dangerous bits.
Yes, I am with you on that. But especially for long carries I prefer my method. But you can also free a hand with that one. You don't have to hold on to the crank or the fork, one of the two is enough.