Not because of their rampages. That would be no worse than any other natural disaster -- that is, it could be terrible, but not peculiar to dragons.
The problem is their hoards. They could lock up a lot of gold and silver and copper in them. Now economists will tell you that you can not increase wealth by increasing money, but they generally leave out -- unless the money is so short supply as not fulfill its function, to facilitate trade. That's why it was invented in the first place, and if there isn't enough, it's a problem. Gold rushes -- or even coining copper coins -- brought more prosperity by making it easier than ever to make trades (and, with the copper, change).
Perhaps they would invent paper money with all its problems sooner. Or perhaps it would be gold certificates, and the gold in dragon hoards would solemnly be considered actually the property of the person with the certificate. There's a place in Oceania where they use enormous stone coins, quarried from a distant isle, and too big to actually move. Even when a boat returning with one was lost, they would transfer title, not actual coins, so the one at the bottom of the ocean worked as well as any.
Then there's the question of what happens when the dragons comprehend paper money. Or even more complex forms, like stocks and bonds. A traditionally minded dragon would be a conservative investor to be sure.