What do you do with the spare tubes and tire levers in the mtns?....j/k...
Never mind that. How about the rope, rack, axe(s), and crampons on the bike?
I'd hate to carry my mountaineering load on my bike. Not that I really like it on my back either, but it's gotta be done. Harder to cut weight when your life is depending on some of the heaviest gear.