Even with some sort of quantum field preserving their 3rd dimension, existing in and traveling thru the richly populated 2 dimensional space as shown they would be leaving a wake of destruction in all those fancy lines etc. instead of leaving the 2 dimensional objects undisturbed. Not to mention to collisions with the other 2 dimensional objects. There would be more to it than just losing their 3rd dimension.

Thank you for noticing.

Season 2, episode “Sanctuary”, hilarious.

Show is coming into its own.