Some years ago I worked in Canyon de Chelly (Arizona) and poked around a lot. It became my invariable practice to carry 60 feet of 3/8" climbing rope, even if no climbing was contemplated. I used that 60 feet from time to time, even without any other gear, and it smoothed out a lot of problems.

If we did plan to climb, naturally we loaded up with the appropriate stuff.

I think you are exactly right to carry some rope in that situation, particularly where weight is a consideration.