Mobile BPs aren't an option if any flight segment is on a partner. Just the way it is - in the industry, I think, but definitely with UA. Always been that way.
On the other hand, on the return (if there is), once checked in and after landing from your last partner flight, any UA BPs for connecting flights in the same itinerary will appear automatically in the app (assuming you can get online, of course).
Not sure why anyone in their right mind would print their boarding pass on 8.5x11 piece of paper and take I to the airport. I always cut mine to the actual boarding pass size, guess it doesn't take a genius to figure that out, or then perhaps in this day and age it does
I usually use mobile BPs from the app, but if I can't, I usually just check in online and don't bother printing - and use a kiosk (or agent) to print up the BP at the airport.