I have two concerns with that, above the (major) technical challenges:
1. we wanted this to be writable using colored pens
2. if we add a dimension, we must add it for real.
#2 is to me the vastly harder problem. Just like in UNLWS, we always have to challenge our own assumptions in order to get a sense for what would be "native to" a two-dimensional written langauge, we'd have to do the same for 3D (or 2.5D). Merely slapping 2D planes together with some links would not come anywhere even close to a robust use of the medium, just like merely having English sentences branch off from each other isn't anywhere close to a robust use of two-dimensionality.
Fully 2D language is already an extremely conceptually challenging problem, at least to me. Hardly anyone has even tried. There are fundamental challenges, like "how do you tell a joke when you don't control the ordering".
I don't think anyone is currently able to do 3D in a way that would truly serve the medium - and the medium would need to be much better defined, since humans' inability to actually see anything 3D instantaneously (we see 2D with an imputed distance and assumptions about what the rest looks like) implies that there must be interaction-in-time of some sort (like, at minimum, moving your head or the object in order to see the whole thing). That's going to be very specific to the medium. Are we talking about arbitrary 3D disconnected polytopes, ants' nest casts, convex hulls, computer-manipulated 2D, VR goggles, ...? Those all have radically different affordances.
Simultaneously, it would trivialize problems in 2D that we have to deal with. E.g. in 3D, there's no circuit wire-crossing problem, whereas in 2D, Borromean rings e.g. have unavoidable collisions. It would be cheating to use 3D in some shallow way to get rid of that issue, without also dealing with 3D's own problems.
Design constraints are a good thing.
