I don't know what the future of the door to door work is but nothing would surprise me at this point. As far as the carts are concerned, I'm sure there is more profit in having the Publishers load their carts full of literature every week or month, instead of the few pieces they can typically carry in their little book bags. Whether the literature is or isn't "placed", is immaterial.
Decades ago when the topic of using television as a means of reaching people with our "life saving message" was broached, they said going from door to door was a commandment and they didn't want to look like the TV televangelists. It doesn't seem to make a difference to them now that the televangelists are also on the Internet just like they are. They even look like they use the same set designers and jewelry suppliers.