You have to evaluate shortcomings as compared to something. You can make a list and say "but InChI doesn't represent X" where X is ranging around
polymers from repeat units
The point is: so what? All representations have some limitations. But limitations aren't shortcomings unless you have a different ...
Your question is rather broad. So the answers can't be too narrow. If you look for material properties like DoS and phase diagrams, try The Materials Project. Working with Pymatgen to brigde to programs like VASP and Gaussian «to compute further», the API is briefly described here.
PubChem now have a REST API serving properties as part of their PUG REST service.
There's a table of available 2D and 3D properties that can be selected, and a variety of input and output formats supported, including database ID, SMILES and SDF input, and JSON/XML/CSV outputs.
For example, to GET a set of properties for a SMILES string for benzene, in JSON ...