Probably the ability to not be an unbalanced idiot 24/7. I literally fell up the stairs twice this week. There are few people who are less scatter-brained than me.
I appreciate the concern, but my problem is more on my ability to concentrate on what's in front of me. I'll be walking around or climbing up stairs while my brain is in la la land thinking about something else. That's normally how I end up clutzing out.
The logic in your post is sound though, I never did think about my core.
But I do work out and I do core workouts alongside arm day and leg day. If anything my core is the thing I'm strongest in.