It's not the text. The text for minor illusion says nothing about moving or not. People are assuming that because the text for major image specifically calls out movement that any other illusions which don't specifically spell out a movement clause cannot move or animate.
My own personal reading is that the movement clause of major image is totally redundant: it's not present, for example, in creation. Are we to take it that objects produced with creation cannot move or animate? How about phantom steed?
I would submit that if the clause was not present in the major image line of spells, no one would rule that an illusion of a creature would be inanimate or unable to move about within the spell's range.
However: the rules pretty clearly state that if you take an action to examine the product of minor illusion, you get an intelligence check against the save DC of the spell. Outside of combat, I would expect that an examination would be automatic. I would suggest that an NPC you expect to be particularly familiar with money would get his proficiency bonus on the check too.
Identification of off coins should definitely not be automatic. Take a look at
https://en.wikipedia.org/wiki/Denarius for some pictures of how much variation there was in official coinage. And THAT is if all your coin are from the same empire. If you're an adventurer, then there's all sorts of crap mixed in there.
In fact, that's most likely the reason this ruse will fail: while we as players use "gold pieces" to buy things, the characters are probably handing over a pile of assorted coins and the merchant then weighs them and bites them and performs other tests of purity, simply because neither the characters nor the merchant have any idea of their worth up until that point.
