Not RTFT but think you're better off boycotting the stuff to wrap than the wrapping itself... Give experiences instead or agree not to do gifts, or make charitable contributions instead to a charity of their choice (I understand this may not wash with children!).
Having said that, we do have some lovely handmade stockings, and don't wrap things that go in there, that is one potential solution.
Bought a second hand Playmobil set last year and we set it up on the table the night before and just put a blanket over it for them to pull off. They loved it, it helped avoid any potential issues with the box already having obviously been opened / ripped, and it was ready to play with right away. We set up garden toys in the back garden for them to "find".
I have used old silk scarves to wrap gifts in the past too. You can usually pick up in charity shops for £1 or less. We have some fabric wraps which we use between our family members only so they get passed around.
I really do love wrapping paper, the way beautifully wrapped presents look and I love doing it myself, so it's not easy to resist and I sometimes worry people think I'm being skanky, but it's just so wasteful.