Would you settle for...a combination of factors?
;)
You're right, though--the Mongols are one of those areas of history where popular interest significantly outpaces research. We can find contributing factors in the primary source record, the practicalities of archaeology, the state of secondary scholarship, and the long stranglehold of "classical" education and adulation in the West.
I'm going to write this from a western, primarily Anglophone perspective, although it will become clear that the specifically Western factors involved affect Near Eastern and Asian scholars as well.
In terms of primary sources: internal to the Mongols, the source record is extremely weak and late. The oldest surviving textual source, known today under the excellent title The Secret History of the Mongols, was written sometime after 1228. Even then, our copy is in Middle Mongolian, but recorded in and for a Chinese context in the early 14th century. Igor de Rachewitz argued in 1965 that the Secret History was an original for the Mongols, not just the sole survivor. Genghis Khan had ordered the adoption of Uighur script for the writing of the Mongolian language, reinforcing our understanding of earlier Mongol illiteracy; the text itself seems to be a collection of oral genres mashed together rather than reflecting any established written genre from surrounding civilizations--and definitely not reflecting the internal historiography that Mongols under the Yuan dynasty would produce.
Later on, even with Kublai Khan's advisors convincing him that the history of the Mongols starting from Genghis' sons needed to be written (the Secret History covered to that point), the segmented Mongol Empire had entire swathes that just...shunned an internal historiography. Thus, even with the Mongols developing an elite literate class within the Golden Horde or the Chagatai Khanate, they seem to have preferred to maintain oral histories rather than written ones.
The other body of Mongol Empire writing that survives is diplomatic letters especially to the West, which exist in Latin translation. But the utility of this corpus for informing us about the Mongols themselves is limited by its purpose, especially since Latin Europe had a vested interest in seeing the Mongols as potential converts to Christianity and allies against Muslims.
Then there are the external written sources from the people who interacted with and reacted to the Mongols. There are lots of these!
...And they are written in medieval versions of Chinese, Persian, Arabic, Turkish, Russian, Armenian, Georgian, Old French, Italian, and Latin.
To really get a grip on the Mongols, a scholar would need a handle on a rather breathtaking number of languages, or access to reliable translations. This is why "how the West reacted to the Mongols", as Peter Jackson points out, has been a rather popular line of scholarship since the 1820s...in the West.
Which leads us to the secondary scholarship problem: it's dispersed among even more languages than the primary sources. Bits and pieces of analysis of the Mongol Empire have absolutely been done! Are ongoing! And often impossible to access for the majority of scholars.
Archaeology, which is ever more important even to historical fields with a strong textual record, poses challenges for tackling the Mongol Empire as well. The Empire was big, y'all. There's not as much "knowing where to look" as there is when, say, walking through Rome. And much of the space the Empire held--including actively held, with outposts and castles--is not very densely populated today. So in England, for example, you've got another medieval village discovered when the city goes to build a parking lot or an apartment building. That kind of serendipity is less likely to occur for archaeologists searching out Mongol material culture.
And finally for present purposes, I'll talk about the overarching, many-tentacled influence of the Western inheritance of classical (Greco-Roman) culture. I was originally going to make a joke about how if you're comparing density of historical scholarship on a subject, ancient Rome is about as useful a metric as the tanks of World War II. But the fact is--that is not a given, that is an active, ongoing choice of European/American historiography. Even with "barbarian" appropriation and alteration of Romanitas in the early Middle Ages, "Rome" as an idea held a certain allure, a prestige that everyone wanted to tie their own polities into. In the 14th century, early humanist writers lament how the world has fallen into a dark age since the high point of Rome; the Renaissance of the 15th-16th centuries was a group of white men wanting to bring back Rome. Rome has been at the center of historiography and the west in more ways than just the immense debt we owe to Edward Gibbon--the whole idea of "western civilization" derives from a culture repossession of 'classical' heritage. Into the 20th century, learning Latin and Greek was the basics of an advanced education; "classics" is not only its own field of study, but monopolizes the label "Classic" for Greece and Rome above the classical traditions of every other society on the planet.
So for Westerners, learning Latin and Greek in the course of a formal education was for so long a necessity because of our belief in the importance of classical heritage...but that also made it much easier to study Greece and Rome because people could read the sources!
And the linguistic imperialism of the west continues today with the surpassing importance of English in historiography. Historians trained in western graduate schools must know English, French, German, and then (or possibly substituting for French/German) the languages relevant to their own research. What if we required historians to learn Arabic or Farsi and Chinese or Japanese, and then allowed the substition of French or German for one if their research demanded it?
In the case of Mongol research, that would connect Anglophone scholars with the scholarly community that doesn't produce writing in English, French, or German. It would provide a basis for tackling a body of sources that is immense when you combine languages.
And it is almost definitely not going to happen. What I said above about how Europeans, and European-descended North America, viewing Greece and Rome as the "foundation of western civilization" since, well, since Greece and Rome? This invents a continuity, a line from them to us (I am American) today, which has major ramifications for scholars having to defend our existence as scholars, not just the conclusion of our research. There are, they say, two reasons to study the Middle Ages (slash Renaissance slash European history etc). One, because it's the foundations of the modern world and lets us see how we got here today. Two, because the Middle Ages are f*cking weird.
If you take a sweeping, people-focused historical approach, as history academia to its credit is starting to/trying to do, you absolutely find the "foundations of western civilization" in a web with other civilizations; it's not a story that can be told in isolation. But the mainstream idea of "foundations" tends to be intellectual, scientific, probably less so religious today. Lawyers drop Latin terms into everyday prose because the roots of our legal traditions are Roman; you're reading this in a font that derives from the 15th-16th century humanists believing that the Carolingian miniscule handwriting their classical sources were written in was actually Roman handwriting.
So ultimately, it's easy to say "the Mongols didn't write much." It's easy to say, "the Mongols are hard to find in the dirt." But look--the Mongols are a medieval civilization, and if there is anything medievalists do better than you, it is drawing entire books and decades-long scholarly controversies out of the doodle marks in the margins of one manuscript, or the discovery of a single coin.
We absolutely could do better. But long, long patterns of Western cultural chauvinism have shaped a scholarly environment where research on the Mongols is compartmentalized in isolated linguistic/geographic communities. And we're a long ways from fully reconciling those divides.
While there is a general Western bias in our historiography, there is also a dearth of information on the Mongol Empire because (a) a coherent Mongolian empire didn’t really last longer than the 13th century and (b) the Mongols were better at adopting culture than creating it.
First, “The Mongol Empire” refers to multiple places, governments, and periods of time. Broadly, we can look at it as:
To your comparison with the Romans specifically, there are plenty of differences to suggest why we might know more about the Roman Empire than the Mongol Empire. As examples:
Duration: The Roman Empire lasted from 27 BC – 476 AD (or 509 BC – 1453 AD if you want to be more expansive). The Mongol Empire lasted for about 150 years.
Form: The Romans always maintained a civilization (literally a ‘culture of cities’) founded on agriculture. This made it easy to expand and reproduce their culture. The Mongols did not originate in cities, and they maintained a degree of nomadism. Their military success was based on that nomadic culture, and the expansion of their empire was certainly based on military success.
Culture: When the Romans subjugated a region, they imposed their culture along with their rule. The Romans brought Latin, Hellenic thought, and religion (importantly, Christianity) to the empire. The Mongols tended to take on the culture of the peoples they conquered. Mongol rulers adopted Tibetan Buddhism and Islam, used local scripts when writing, and employed skilled non-Mongols as civil servants, siege engineers, artisans, merchants, and diplomats.
As a civilization, the Mongol empire fits within the framework of their subject peoples more readily than into a uniquely Mongol framework. So if you write a history of medieval China- including a Mongol period- that will form a more compelling narrative than a Mongol history which includes a Chinese component. Likewise, you can write a history of medieval Persia, India, or Syria and include a distinct Mongol period in each one.
And that’s what historians have tended to do. Each of the Mongolian hordes in those respective countries took on the characteristics of the subject people, including language, dress, religion, and architecture.
As an example, while the Mongols slowly conquered the Chinese Song dynasty- replacing it with their own Yuan dynasty- their Chinese subjects became increasingly devoted to their own native interests and culture. Confucianism had a renaissance in Chinese thought. A distinct form of blue and white ceramic was popularized during the Yuan dynasty. Important Chinese inventions spread during the Yuan dynasty, such as paper money, gunpowder, the compass, and large two-story looms. It’s interesting that all of those things predate the Mongolian conquest, but they were far more common at the end of the Yuan dynasty.
To get a feeling for what the Chinese thought of Mongolian society, when Zhu Yuanzhang overthrew the Yuan dynasty he named his empire “Ming” meaning “bright.” Its character is an ideogram of the sun and moon, being all the light of the world. For him, the Mongol conquest was China’s Dark Age.