This is the other way that they can tax bitcoin and other crypto transactions but there could be other ways that we haven't think of. It wouldn't be decentralized anymore if they will require everyone to be registered as a bitcoin and cryptocurrency enthusiast because it's against from what bitcoin is intended for. But we have no choice if this is going to be the system that they'll implement.
They'll ask for the record of that local exchange and file taxation for those users that have made profit on that exchange. If they'll not voluntarily go to the tax bureau, they'll be the one to inform the user that there's an associated bitcoin tax record that should be paid.
Imagine if government taxed bitcoin and other cryptocurrencies, what if all the fiats have already been converted to crypto? Where could the taxes could came from? That is why we need to devise a plan and law for the taxation of cryptocurrencies though, its quite ironic to tax crypto which in fact, on its protocol do not allow any third party to do so, I think we need a whole new civilization that could still propagate without tax if cryptocurrencies could be accepted world wide.