Democracies relying almost exclusively on a single export for their GDP?

Well, RBR, as you know, these are usually former colonies -- that is why and how they were colonized -- and many of these are politically unstable, but the export situation is not a cause. Similarly, I doubt that those former colonies who are more politically stable owe it to a diverse economy rather than to, say, sound institutions. I think Costa Rica and India are examples of good institutions, not diverse economies.

Alaska? (oil). Venezuela? (oil). New Zealand? (Lord of the Rings) Nauru (phosphate). Much of the Caribbean- either banking, rum, sugar, or bananas. It's a small list to be sure.

I suppose it's right to ask today if, other than oil producers, there are really countries out there without a "diverse economy." Is your data set entirely composed of oil producing nations?

I suspect, however, that we are all oversimplifying. Saudi Arabia and Kuwait are oil-producing wastelands, but Iraq is in ancient Mesopotamia. It has agriculture and a civilzed, urbanized population that has been the center of empires for as long as there has been civilization. Iraq probably has probably never been as dependent on oil as we suppose. Our figure that 95% of Iraq's exports are oil is somewhat slanted by the past 13 years of sanctions where the oil-for-food program was supposed to be the main exception.

What do we know of Iraq in the 1970s, before the Iran-Iraq war forced it to turn to gov't-run, cash-producing oil?

Here is something taken from Al-Ahram, the Egyptian newspaper:
"Since the 1970s, Iraq's agricultural sector has been badly administered. During the 1970s Iraq was by far the largest supplier of dates, supplying 80 per cent of international market needs. By the 1990s, Iraq's exports had dwindled to an alarming degree. Importing fertilisers and plant parts have been difficult under UN sanctions. Sanctions have also stopped the import of certain agricultural machines and equipment, because they may have a "dual use". Iraq's livestock is afflicted with various diseases, which lowers agricultural output and limits access to meat for food."

Perhaps the Ba'athist regime encouraged a non-diverse economy, rather than the other way around.