The buckets are more flat than sharply defined (ha). That's part of the problem. Information is lost from notation to pitch to recording, and I suspect one coul

The buckets are more flat than sharply defined (ha). That's part of the problem. Information is lost from notation to pitch to recording, and I suspect one could prove that these transforms don't preserve topology and are not homophormisms that can be easily reversed. To use your example, finger position is not a one dimensional subspace on a guitar. There are between 1-6 ways to play a given pitch even assuming standard tuning on a six string guitar, which is not a safe assumption to make. But the issue with chord transcription is one at the heart of source separation outside of VC demos, which is the causality problem that no one likes to talk about. To separate into N sources you need to know a priori that there are N sources to separate into. This is not a trivial thing to predict in chord voicings, where N changes and is not predictable. Then you need to make a best guess at which instrument the pitches fall into, which may be shared. This is something that even humans fall victim too. Untrained listeners are very bad at quantifying sources in an ensemble, and even trained listeners struggle with notating chord voicings with decent accuracy.