1) I think nowadays documents like invoice/BE, TDS certificate etc (original/signed/hard-copy) have lost their sanctity, in respect of most of the transactions, though not explicitly mentioned in the respective statutes.
2) For example, in case of GST invoice, since the transaction are uploaded by the other party, I think insisting on hard copies would no longer be a necessity. However, if transactions are such that they cannot be verified by this method, then I think original, signed documents are required to be maintained.
3) This is very similar to TDS certificates as nowadays no one really asks for it as such transactions automatically get updated in 26AS.
If transactions can be verified by other permissible means then I think soft copy would suffice. If we are able to maintain hard copies in most of the cases, exception with regard to soft copies (in some cases as above) is acceptable during audit too I think.