I distrust any blanket assertion that such things are "technologically impossible." I'd agree to "highly improbable", given the ridiculous frequency with which consumers' or citizens' private data is regularly leaked, by corporations and government agencies alike. And given the stupidly insecure and inaccurate electronic voting machines we've seen before, I'd say it's probably "impossible" for some companies to create a secure system.
But properly working, secure authentication and crypto is a thing. It's damned hard to get right, but it's not impossible. At some point, we'll probably figure out how create a system that uses authenticated electronic ledgers to prevent fraudulent tampering (blockchains, etc) while still preserving anonymity. Still, until we figure out how to put such a system in place and make sure it's reasonably secure, paper ballots are at least a bit harder to manipulate on a mass scale, although still not impossible.