Unfortunately such systems assume that all of the parties in the election are working in good faith towards finding out the true result. They don't deal with the threat model of one (or both) major parties deciding to deliberately cast doubt on the outcome of an election by lying about or losing one of the secret keys needed to check the results.

Even if all the parties behave correctly, it's still not clear that such a system is really solving the underlying problem. If someone claims there were thousands of fake votes sent in by dead people, are you really going to reassure the public by saying "Don't worry, we've re-calculated the modulo-n equations using the cryptographic key's bitstream acting as a stream cipher"? That's just asking for the backfire effect to kick in.