I must confess, I can’t visualise what you’ve described.
Darn it, it was supposed to be just a pet theory… 
I must confess though that I will have to get me a model and/or make sketches about it, but of course, the reason why I’m not too invested on it is that it could be wrong; but I’m curious enough to try, I will report later.
Again, I would think that the Romans did not care about giving everyone the same odds, could be that the knobs are there to also allow the item to not roll much or to get stuck on the ground… with a clear “winner” or “fate”. The bigger the size, the better for a group of soldiers on the march to see clearly who was going to be the bait that day. (Taking into account the locations they are usually found)
How sure are we that they are found more often in military camps? My understanding is that most have no context. That is, they were found by people who were not archeologists and who didn’t know what kind of Roman facility was at the site. Of those we do know, a plurality were found in military camps, but that number is something like 5 out of 12. So I think attributing them to a military use is not necessarily accurate.
As far as the idea of them being a die, I have severe doubts. Did anyone even propose the die idea before dodecahedra were used in modern role-playing games?
That’s fine but it’s totally irrelevant to my question. Did anyone propose that the Roman dodecahedra were used as die before D&D used d12’s?
Actually, yes.
Some of the various theories as to their use include children’s toys, gambling games, or fortune-telling devices - perhaps they were thrown and their faces read like that of dice. However, experiments with reproductions show they are difficult to roll.
Now here is where I think many are getting it wrong, when dismissing the gambling or fortune telling theories (with a religious component too IMHO), many researchers are applying modern ideas of fairness and provability on a device made by people that did not knew about them or cared, as shown with the Roman approach for dice making too.
You think Roman gamblers wouldn’t have known or cared about the concept of fair/weighted dice?
Here is another article pointing to the way ancient Romans did not care about using unfair asymmetric items like dice:
In Roman times, according to the research, the difference in the sizes of the sides could impact the odds of a single die, on average, anywhere from a modern-day convention of 1-in-6 to as much as 1-in-2.4.
The researchers believe the disregard for probability came from the belief in fate ruling the day. Researchers had 23 modern-day students place pips on reproductions of the asymmetrical Roman dice, but without any explanation as to why (that way they couldn’t cheat). Every one of the students in the study started with a 1 on the largest side, which meant the corresponding number added a 6 on the other larger side. Researchers figured this was simply a matter of ease, both from putting the largest number on the largest face and the fact that people start in chronological order.
My point here is that this unfairness (and magicians or augurs having some knowledge about that unfairness) is what allowed some people with power then to control the fate of others. I think that there is a connection to the dodecahedrons, they were used for very special occasions, first with religious or magical reasons, and then the fad moved also to gambling and then the smaller jewelry versions; used to also increase the luck of the wearer in their minds.
I’ll also note that it’s possible to create a fair game using unfair dice. For a simple example, player 1 and player 2 each roll the die, and the higher roll wins. In event of a tie, you double the stakes and roll again. No matter what the die, the two players both have the same chance of winning.
Do the rules of any Roman dice games survive?
Based on the shapes of dice cited, usually no, they did see even the misshaped items as part of their fate. And IIUC, if the others used the same dice, then the chances equalized.
Could it be–one half of something else ?
Maybe you jest, but I think the missing part are the pieces (with an also missing holding device for the pieces that was inside?) and the way those used the holes and the knobs.
They’re found in the region that the Roman Empire was expanding into, from the approximate time when that expansion was happening.
On the one hand, that might be seen as evidence that they had some military purpose.
On the other hand, military purpose could be argued for any and every Roman artifact found in that area dated to that period, just because thats what the Romans were doing there at that time.
There is the question about why here, and not in the other places the Romans were annexing around the same time.
It just sounds unnecessarily complex. If you want a fist-sized 12-sided novelty die with wooden faces, would your first thought be that we have to make a hollow bronze form with knobs on, and different sized holes in the faces, then engineer a system of hooks and clasps to affix the wooden faces to the bronze form?
I think not. You’d take a block of fine grained wood and carve it into a dodecahedron, and done.
I don’t want to dismiss the gambling/fortune telling theme, because that seems like a possibly productive avenue, but it just seems to me like this thing was never made for throwing at all.
One question I haven’t seen a definitive answer to is this. Do all the dodecahedra sit on all 5 knobs (or at least sit without rocking) in every orientation?
There seems to have been an implicit assumption that they do. But as noted earlier, this is not a trivial thing to get right. How well the knobs are positioned might tell us something about the intended use. If they are well aligned and the thing sits well in all orientations we might reasonably assume that this is an important part of its function.
If you were making something to be handheld in use or supported on something like a pole or staff, there would be no point.
The best (that is, the most finely-crafted and intact) examples do appear to sit flat on all five knobs, but that could just be a function of them being well-made and therefore regular.
I did find a photo of one that appears to sit on four knobs with the fifth one cocked by a millimetre or two:
It still looks to me like that was intended to sit flat on all five; it could be that it was distorted in casting or it could have been damaged.
I just spent a little while looking at examples of ceremonial mace heads. A mace is a weapon, but there is a tendency for ceremonial versions of the weapons to be iterated into more fancy and less plausibly functional over objects over time.
A lot of bronze mace heads (Roman, or adjacent cultures) prior to the period of manufacture of the dodecahedrons have a sort of geometric nature to them, or have knobs on (as a function of being a weapon, or derived from a weapon). Here are some from Iran https://www.ancient-art.co.uk/near-eastern/rare-luristan-bronze-mace-head/
https://p1.liveauctioneers.com/3779/269152/140817204_1_x.jpg
https://p1.liveauctioneers.com/3779/269152/140817202_1_x.jpg
Again, if you read the cited investigation about dice, Romans did not care much about fairness, when looking at the Roman dice it is clear that they did not want for those things to roll for a while.
I can grant that one does not have to be so complicated, it may be then that the pieces added were pentagon pieces of cloth or leather with loops in the corners that could be added to the faces, and hold them with the knobs.
That granted, I would still not dismiss complicated ways to add pieces or devices that only could be used by augurs that are complicated. Romans could do complex things.
Nobody said the Romans couldn’t do complex things. Doing complex things for no particular good reason, when there is an obvious, simple, existing solution, is the problem.