Right then!

There are a few bits of this question that I need to deconstruct in order to answer it, but this is not me thinking of you as stupid for asking it, and it's clear that you have familiarity above many other people with some of what you've namechecked here.

So I'll begin with one assumption folded into the question- conflating the opulence/richness/urban nature of Bactria itself with the Greco-Bactrian Kingdom specifically. This is, I feel, part of where your confusion comes from. Yes, Ai Khanoum is the only urban site dated exclusively to the Greco-Bactrian (and Seleucid) eras that has been found so far. But there are Greek layers (many of them yet to be fully explored) in Balkh, Termez, and Samarkhand (Samarkhand is in Sogdiana but I'll discuss that in a moment). These are also not the only sites with Hellenistic era layers either, and there are other sites in which temples and fortifications have been found. There are also new excavations due at Balkh imminently, and I'll deal with the archaeology of Bactria properly below. In addition, casting our eyes backwards gives us the Bactria-Margiana Archaeological Complex, a complex agricultural society living in Bactria/Margiana during the Middle Bronze age. This is the period that the oldest irrigation canals in the region come from, by the way. We also find Achaemenid occupation, and indeed most of our few Achaemenid administrative documents not written in cuneiform come from Bactria. And post-Greco Bactrian kingdom we also have the Kushans, for whom Bactria was a core part of their Empire (they used Bactrian language on coinage and we also find the first flowering of the Bactrian language in this period).

There is another area of confusion here- you have conflated Bactria with the territory of the Greco-Bactrian state as a whole, and therefore talked about Bactria as essentially a country of nomads. This could not be further from the reality. The specific region of Bactria has been urbanised and carpeted in high-density agriculture from the Middle Bronze Age onwards and never really looked back. We find evidence of Bronze Age canal-based irrigation and dense settlement, and it is therefore clear that Bactria was a highly populated and wealthy region long before the Greeks set foot there. We find a lot of archaeological evidence for Bronze Age trade between the region of Bactria and Elam as well, and evidence in the Achaemenid and Hellenistic era of Mesopotamian deities having transmitted to Bactria- one Achaemenid parchment from Bactria unequivocally refers to a Temple of Bel, for example, and we find the goddess Nana abundantly well evidenced there. The actual region of Bactria itself has always been concentrated on the fertile alluvial plains of the Amu Darya/Oxus River, or on the oases that pepper the landscape south of that river. The territory of states based out of Bactria has, however, included areas that were much more sparsely populated- the Achaemenids had at least some territory/dependents in the Saka/Scythian peoples north of Bactria and Sogdiana, and Sogdiana itself seems to have been less densely populated than Bactria. Likewise the Greco-Bactrians controlled Sogdiana for some time and seem to have hired Scythian mercenaries on at least one occasion. But to characterise Bactria itself as essentially a country of nomads is a mistake. Chinese visits to the region estimated a population of at least two million people. The country had a large agricultural surplus, though likely not on the scale of Egypt say. The region also remained populated well after the Greco-Bactrians- I've already mentioned the major role it played during the era of Kushan control where it was a major centre of Buddhism, and it was also highly populated at the time of the Umayyad takeover. Samarkhand was a proverbial city of splendour and magnificence for a very long time, and is an argument against seeing Sogdiana as an essentially 'nomadic' area as well. Samarkhand was the centre of Manichaeism, and later the site of the first paper mill in the Islamic world.

You are also slightly assuming that Ai Khanoum is the sole Hellenistic era city excavated because it's representative. Ai Khanoum was the first Hellenistic era city located in Bactria, and was excavated for almost a decade, but excavations have not been possible in Afghanistan for 40 years because of everything from the initial Afghan Civil War onwards. The majority of what was ancient Bactria has been totally unsafe to excavate, and so excavations have been concentrated in the areas still safe (i.e the Central Asian Republics). Nor was there a long history of archaeology in the region prior to this; unlike the Aegean and Egypt which have a very long history of archaeological excavation, Bactria is young. It only became an area of interest in the 1920s onwards, and primarily to French archaeological teams. Ai Khanoum was first discovered in the 1960s, and excavations were forced to stop in the 70s. The awakening of Bactria as an area of study rather than simply a curio is barely half a century old. However, what archaeology we do possess for Bactria indicates that yet more awaits us.

This brings me onto another topic- why would even our current archaeological information indicate that Bactria was ever rich in the Greco-Bactrian era? I've talked a lot about other periods, but less so the Greco-Bactrians specifically. However, even the barebones archaeology and known history of the Greco-Bactrian kingdom indicates a powerful, opulent state. Prior to any real urban archaeology we already had an immense amount of Greco-Bactrian coinage. Between this and literary references to how rich Bactria was it created something of a meme in the 1950s; in the period when serious exploration was underway but no urban site had yet been found it was referred to as a Bactrian mirage, because so many other signs pointed to an important kingdom and Greek presence in the area. The single largest coin minted in antiquity comes from Bactria. We have hundreds of bronze, silver, and gold issues from the Greco-Bactrian kingdom regardless, many of these coins evidencing kings unknown elsewhere in our surviving histories. Another quote of yours I have to disagree with is 'its brief existence'- the Greco-Bactrian kingdom existed for almost a century. Nor did it initially lack for military successes- the state successfully gained independence from what had been the world's largest state of c.300-200 BC (the Seleucid Empire), was never militarily subjugated by Parthia, resisted a siege of its capital by a Seleucid royal army for a year and gained recognition of its monarch's status, and occupied much of North-Western India. Even in the final years of Ai Khanoum's occupation we find evidence of massive deliveries of Indian coinage to the city. And now let's move onto Ai Khanoum- the city is enormous. It's a full 1.5x1.5km in size, dominating the confluence of the Amu Darya and Kokcha rivers. It has the largest known propylaia of any ancient Greek city. Its beautified, municipal architecture nearly all dates to the period after the Greco-Bactrian kingdom had declared independence. We're also fairly certain that the city had a mint. The inhabitants remained in cultural contact with the Mediterranean despite the growth of the Parthian state. Within the city was found unrefined quantities of lapis lazuli, indicating it to be an economic hub as well as a militarily strategic site (and I will return to that extraordinary mineral in a moment). Its walls were enormous and refurbished multiple times over the kingdom's lifetime, often extensively. Any hard stone used in the city's monuments and other buildings would not have come from the immediate area of the city, and the nearest source would have been many miles to the north. Our surviving evidence indicates Ai Khanoum as the central hub for significant tributary relationships with India, and as having a significant bureaucracy incorporating both Iranian-speakers and Greek-speakers within.

However, there's one final question that lurks- what would have been any basis for Greco-Bactrian wealth? Or Bactrian wealth in general? Aside from agricultural production, leading to dense population and leading to high tax revenues, there were other sources of revenue for a controller of this region. For one the region was the only source of lapis lazuli until very recent times, a highly valued pigment and semi-precious stone. This is the source of the somewhat infamous ultramarine blue that was so expensive for painters to acquire in the 12th-19th centuries AD, for example. It is also a region rich in gold mines, and was also a source of spinels (which are often misrecorded as 'rubies' in the same way that the conflation of sapphires with lapis lazuli can be very confusing in older sources). It was also, in this period, the main overland route linking Central Asia to the Near East and India to Eurasia in the North and East- via both camels and river-routes. Camels are attested on BMAC art, but we're even more sure of their importance by the Achaemenid era in which the harassment of caravans is a matter of concern to the Persian satrap of Bactria. The Greco-Bactrian kingdom could then add to tax and trade the matter of warfare. Expansion of the Greco-Bactrians is not fully understood, and it is somewhat difficult to know which of the few literary sources to trust, and how to interpret numismatic evidence. What we can be sure of is Greco-Bactrian expeditions into the collapsed/ing Mauryan state and conquered a large swathe of its North-Western territories, and that Ai Khanoum indicates a continued economic relationship between Bactria and Indian states, one which resulted in the latter being enriched. Unravelling the byzantine state of Indo-Greek kingdoms and rival dynasties post-180 BC is a zero sum game, unfortunately, or I would comment on that more.

I hope any of this has been helpful to you.