Yes, there is a planck length cubed, but you can't obtain relavant symmetries to call a 2-d theory as one which satisfies the 3-d case. It really is as simple as that. 2-d is an oversimplification.
Well I agree with that because you are missing all the data from the 3rd dimension if you use a 2-D. There is no 2-D manifold that can contain all the information exactly of a 3-D space.
But even if that is the case you are still missing the information inside the 3-D shape when you take it 2-D.
Edited by VictorMedvil, 01 July 2019 - 12:10 PM.