With only one or two exceptions where I like to keep print copies around for reference (or for travel use where I want something disposable–don't want to leave an iPad on the beach or by the pool, for example), I'm the same as you: it arrives, it goes straight to recycling, and I read it on my iPad/Kindle/whatever. Last year I went on a tear, trying to stop all paper delivery while retaining digital access.
Turns out very, very few publications were helpful. Everyone understood why I wanted to do it, but they make their ad money off of paper copies shipped. So, as with the Economist, you have a lot of rags who're talking the talk about conservation, provided it doesn't cost them a penny.
Sure, they'll charge the customer more for less.
A couple were great about it: a quick email and it was moved over to Newsstand, or their app, etc. But the rest, the bigger publications, almost uniformly baulked, and could never make it happen.
I even considered trying to shame them by creating a site so everyone see who's forward-thinking, and who's myopic. I may yet.
It kind of reaffirmed my view that the whole print industry is a broken model. The end result is that I canceled a bunch of subscriptions, since the ones that are supposed to have credibility about world affairs just lost it in my eyes, I couldn't take them seriously (not that I ever should have).
It's also made me extra sensitive to the whored-out nature of publications that take ad dollars.
As a result, I canceled a bunch of subscriptions, and focused my energy on the ones that operate from subscription models (which are more expensive individually, but I saved more than that getting there).
Turns out I'm getting better information, paying more attention to it, and don't have a stack of magazines to worry about recycling every month.