I agree with you that technically it can be done. Which is why I said:

"I don't want the government's aim for auditable provability"

I mean, technically they could do it and provide at least a modicum of privacy protection. But I will bet they won't because whoever is implementing it will want to be able to point to specifics - specific people, specific times, specific places - so they can cover their arse come the next moral panic moment.