I think you don't want thick stacks of logic. But DRAM and NAND have been getting stacked for a while.
I think there are way too many interactions between those layers for stacking to be a viable alternative to the conventional layer sandwich. Stacking has overheads, if you'll excuse the pun.
Silicon atoms about about .132 nm, and any design logic is probably going to need 2 or 3, so we are looking at 1nm actual size as the lower limit for silicon. 2D materials might cut that in half, but that would still have a limit we would reach very soon. And I don't think they are talking about making A4 letterhead size chips. At some point they will have to be stacked to keep progressing forward and utilize existing packaging techniques. Not to mention stability and ergonomics.
As to the flat surfaces, that is what electron microscopes are for. You just shave layers off a block of silicon until it is flat enough for their confined growth technique (which I'm sure they did). They are more or less talking about self assembling circuitry via selective crystal growth as a means to mass produce 2d materials to a specification. That material's interface to the outside world is likely to rely on lithography and more typical silicon substrates and techniques.
I get what you are saying about putting the layers too close together, but the whole idea might be that said layers could be part of the logic too. Laying out a regular grid of P and N type materials is one thing, getting them to do something might mean connecting them from top or bottom, or likely both.
If you look at CMOS sensors or HBM or AMD's 3DVcache it is pretty crazy layered stacking already. And some of that is lithography to burn out trenches and things and the deposition layers with doping chemicals, and the actual surface polishing to remove back down to the original layer, and repeats to build out silicon vias. Pretty crazy.
I don't see anything wrong with applying the same thing to a 2D layer.