Well, either I misunderstand 1x or cross chaining. With one sprocket in the front, and a bunch in the rear (my understanding of 1x) I don't see how there's any cross chaining.
Yes, it depends on how you define "cross chaining". I contend that the chain spends more time at higher angles in a 1x system. As I said, if you have a 1x system with a 40t chainring, on the road, you'll be spending a lot of time in the small cog with a fairly extreme chain angle. Whether you call that cross chaining or not, it's still an extreme chain angle and will have the drag and increased wear that comes with that chain line.
(sorry, kind of derailing the thread here.)