[Formendacil]

And time is a factor here--it was a millennium from the fall of Arvedui until the War of the Ring. Although I'm sure old Arthedain coin would have been accepted, that would be like American pioneers accepting coin from Alfred the Great's time--sure, they'd accept it if it was good metal, but that's a looooong time to survive in bulk. To an extent, no doubt, the coin kept circulating, but even if it diminished slowly it WOULD diminish--and wear.

Although Tolkien says that the "only" elements of government in the Shire were the postal service and the Shirriffs, I think it might not be too far out of the way to posit the possibility that there was a mint there. For one thing, it's already been noted that the Hobbits worked with silver. For another, it is conceivable that this mint was already there in the early days of the Shire, under the authority of Arthedain and that responsibility for it was assumed by the Thains after the fall of Fornost.

On the other hand, although I think the Dúnedain = Romans equation is a good one, perhaps we should look to the Dwarves rather than Arnor as the chief source of coinage in Bilbo's era. After all, we know that the Dwarves worked with gold and silver and we also know that they had a long tradition (going back to the early Second Age at least) of developing symbiotic relationships like they had in Erebor with the Dalemen: that is, a relationship of Men who provided them with food and horsemen, etc. It is also very easy to picture the Dwarves, with their concern for just payment (cf. what they owed Laketown in their negotiations with Bard and the Elvenking), having a solid reputation for consistently pure coinage, which would be accepted wherever Dwarves were known.

What is more, Dwarves moving east and west along the Great Road are the only known source of outside commerce in the Shire--a far more plausible source for coin than a sporadic filtering up from Gondor (though this may have been more common before Tharbad was finally abandoned--one gets the sense there used to be somewhat more traffic up the Greenway before the Fell Winter).