I don’t see how a Tally stick results in non-anonymous transactions. It’s just a basic way to create an arbitrary non-fungible physical token, just like a door key.
The authorities holding the sticks are acting as a public ledger, in that they bear witness to person A originally handing them half of stick A — and they could write that association down, if they like (picture a little tag saying "person A" wrapped around stick A in their stick storage closet); but even if they don't write it down, they may just remember the person, remember the probably-pretty-unique-looking stick, and mentally associate the two.
Then, when person B comes around with the other half of stick A, they won't know all the hands it passed through in the meantime, but they'll at least know that person A and person B were connected through some chain of equal-value trades that didn't require "breaking" the stick.
Yeah I’m not seeing people being so dreadfully about “authorities” knowing who random people happened to participate in an arbitrarily long line of trades as being a big factor in people moving to gold coinage.
Notable people resorted to things like Tally sticks when actual physical currency like gold was in short supply. So the idea that people moved from Tally sticks to gold due to concerns for privacy just doesn’t hold water. Especially given gold as currency predates Tally sticks.
