I don't like cross tying , either. The horse has pull on two sides of his head, thus can feel more trapped. When he moves off the pull from one side to get a release, he bumps into the pull from the other side, so can bounce back and forth from pull/release to pull/release , and not find a good peaceful place to be.
not all horses will have this feeling, but some do need to be able to move a little and find a release.
Straight tying allows them to move a little, if they hit the end of the rope, they can move off of it without hitting another rope's end.
If a horse HAS to move, he's gonna move.