It wasn't even minted by the 300s. There were multiple attempts to replace it with a new stable silver coin but none were very successful.

> Well, for one thing, most people wouldn't be able to afford a single gold coin. You might collect taxes from a province in gold; you're not going to collect taxes from a person that way.

Well yes, that was a significant problem. Often there was no other choice than to collect taxes in-kind and then the tax collectors either had to find local uses for all that stuff or sell it for gold that could be sent to the central treasury in Constantinople.

By the 500s the Empire was mainly only minting gold and bronze coinage which of course was very problematic (as you said gold is much too expensive for most transactions while bronze has the opposite problem). There were no stable, widespread silvers coins that were continuously minted until the 800s or so (Miliaresion) and then its value collapsed again after a few centuries when they went back to debasing during a period of economic crisis.

> There is no way for such a rare coin to be central to the functioning of the system

Well.. I accept that this is your opinion. Regardless, that's simply not how the Roman/Byzantine Empire worked. Gold coinage (or using gold solidus as the primary unit of accounting) was absolutely integral to its functioning. (moreover it was also central to international trade)