Shrek actually is challenging to stage. You need to do the Fiona transformation sequences very quickly. Plus, there's the giant dragon, Lord Farquaad's absurd height, and the dozen or so fairy tale creatures who pop in and out throughout the show. It's not such a ridiculous choice.
I'd go for City of Angels, myself. The dual role-cast, black & white versus color, aspect is a challenge, for sure. Then there's the two transformations in the middle of "You Can Always Count on Me" and all the reversed dialogue and prerecorded material to incorporate.
I don't know if they are hard to stage, but you don't see too many professional productions of Funny Girl or Evita. No one has the voice power and/or uniqueness to play those parts anymore
Plays that are hard to stage usually involve lots of props and stage business. One example would be "Steel Magnolias" in which hair has to be washed and set with rollers on stage all in a specific amount of time. Another would be "Balm in Gilead" which takes place in a diner with a fully functioning kitchen with waitresses serving food at specific times while multiple actors talk over each other. Also, the opening of "Into the Woods," which is not necessarily difficult to stage, takes hours to tech.