The theoretical argument seems sound, but it does ignore there are massive constant factors in current implementations beyond just the theoretical limit alone (particularly cost and heat) and skips directly explaining why those end up having similar growth rates.
The actual formula used (at the bottom of the ChatGPT screenshot) includes corrections for some of these factors, without them it'd have the right growth rate but yield nonsense.
I guess you're right in a purely geometric sense. It's just that it seems almost silly to consider that given that (AIUI) the 3D geometric constraints don't impact the memory access latency at all for now (and likely for any reasonable period of time).
Like you said, thermal and cost constraints dwarf the geometrical one. But I guess my point is that they make it a non-issue and therefore isn't a sound theoretical explanation as to why memory access is O(N^[1/3]).