A supporting tidbit that I didn't see mentioned is that these seem to appear not long after the switch to a 12 month calendar. Julius Caesar made the 12 month calendar official in 46 BC, and the earliest of these cubes appears around the 2nd century AD (though I saw a couple sources mentioning the first century).
The abundance in military sites still seems consistent. Up until then, the calendar was held in alignment with the seasons by adding months, nearly at random (for example, they were sometimes used to extend/shorten the tenure of politicians). They basically ignored 50 or 60 days a year, and made months up to cover that. If you're away at war, you don't get those messages, and your calendar no longer reflects the seasons or anything.
If I were taking a wild guess, I agree it's a calendar, and I would specifically guess it was used for pay schedules for the soldiers. Rome started paying its soldiers around the end of the 2nd century BC, and they paid monthly from what I can tell.
The evolution seems natural. Rome starts paying soldiers. Soldiers get upset that while at war, their months don't line up with Rome's months due to not getting the memo about randomly added months. Rome institutes a standard calendar for many reasons, one of which is to stop having hoards of armed people angry about not getting paid correctly. Now that the calendar is standard enough to follow while away from Rome, a device is invented to track the months so that soldiers get paid on time and it feels more transparent than the "just trust me" of old.
I think it also provides an adequate explanation for why they were made of expensive materials. The calendar was not just for tracking time, it was directly associated with the wealth of the Roman empire, their ability to pay their soldiers. It's more reassuring when they guy with the brass calendar says you'll get paid on time than when the guy with a wooden one does it.