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I've been carrying my U lock in or fixed to the back of my backpack, and recently had a bad crash falling off the bike and landing on my back fracturing two vertebrae making me reconsider this practice (I'm not sure the lock had anything to do with the damage).
I'm installing a D3O Level 2 plate in it, think that's enough to stop worrying about the lock? Unfortunately I'm a serious fashion victim and can't use a frame mount.

That's how I carried mine when commuting. Towards the end of my commuting days, or if I have errands to run, then it goes in an inside pocket on the bag.
I'm a total fashion victim too with an overly massive Chrome bag. The amount of crap I could carry would crush a small car if I had a collision.
I broke a rib landing on a cable lock in my back pack. They now go on the frame or in a pannier bag.
I'm thinking that attaching the lock to the side of the back could be safer. hmmm.
If it's a regular ride just leave the lock chained up to where you are going to lock the bike. basically stop carrying it! buy another lock for occasional duties.
I’m thinking that attaching the lock to the side of the back could be safer. hmmm.
landing on the flat side is going to be preferable to landing perpendicular to the lock.