InChI is not designed as, nor can used for, what you propose. Last I checked, conversion from an InChI to a structure format was not a supported option, and only exists for testing purposes. Which is not to say that people don't use for that. (Also, last I checked, there are inputs which cause InChI to segfault. And there's no spec for how to interpret InChIs other than to run the reference code.)
The InChI normalization step may also change the chemistry. For example, it may put things into a preferred tautomer form or charge state. This is essential for its goal of linking disparate records, but it is not chemistry preserving, and can be worse than passing an SD file to your nanomachine factory.
It was designed as "deterministic ID for sharing", yes, but not for sharing structure information but rather information related to the structure.
The most "concise" solution is to record the positions of the nuclei and the total charge. Then any quantum mechanics program will be able to reconstruct (to the desired level of approximation) the electron density of the molecule. This is the one you reject.
For good reasons. As you say, you want a nomenclature that can help with identity and similarity, and electron density is a very slow way to do that.
But such nomenclature is driven by human concepts. Fundamentally, there are different reaction rates depending on the relative orientation of two molecules. We see this in molecular beam experiments. For example, from 1979, http://www.sciencedirect.com/science/article/pii/00092614798... "Molecular beam reaction of K atoms with sideways oriented CF3I".
InChI doesn't have a special name for "sideways oriented CF3I", even though a complete, concise system would have to be able to provide a name for it.
Instead, we've come up with concise approximations - a SMILES string, a bitstring fingerprint, etc. - which are tractable for the purposes you want, so long as we stay within relatively normal chemistry. But it's still humans who categorize things into, say, "aromatic" or "chiral", so our approximate nomenclature has to partially encode how humans think of chemistry.
The Game of Life is much simpler than the Reality of Life.