Chinese definitely had a shitton of documentations in terms of historical records and publications. they invented paper and mass printing first, to keep that in mind. However, the Western history is much more Euro-centric, and that part of the history is covered really by Asians themselves. But Chinese did have a lot of documentations too.

Speaking of Greek civilizations, the Archaic Greece was the one with fewer documentations and stuff like Iliads among others were passed down through oral traditions, and weren't consolidated after Ptolemaic Egypt. The Greeks didn't have access to writing again(to note, before the Dark Age the Mycenaean did have writing, only it was also extremely limited) until the Phoenician alphabet was introduced to them, upon which time I believe there were still less writing than we would have liked.

In my experience there actually isn't more extensive documentation of Greece and Rome, it's that our culture traditionally values those two cultures as 'classical' and focuses on them heavily.

With cultures like the Sumerians, it's not just that they were extensive record keepers, it's also that they primarily wrote on media that lasts for thousands of years, i.e clay tablets. It isn't just the Sumerians that this applies to, either, the same applies to the Mesopotamian cultures until writing with ink on papyrus and parchment grew more popular. The amount of material we have on 7th century BC Assyria alone is embarrassingly detailed.

Roman and Greek documentation that we have to hand is far more extensive than for many contemporaries, particularly in Europe, but we actually have far more available information in many areas on ancient Mesopotamia. It gets to the point with archives like that found at Amarna where we can read private diplomatic correspondence between states.

Neither would I agree that Egyptian, Indian, and Chinese history is particularly poorly documented compared to Roman and Greek. We are not quite as deep on any one Egyptian period as we are with, say, Classical Greece, but there is a visible literary record stretching three millenia involving ancient Egypt, and I think there's a far larger amount of Indian and Chinese historical material than you've been exposed to. The issue with Indian sources of any age is that they tend to have a degree of politicisation regarding South Asia's current cultural and political realities, and the historiography is an absolute mess.

To put things into some perspective, we only tend to have preserved literary sources from the Roman period dating back to the 2nd century BC, and we only begin to have a profusion of Roman literary sources from the 1st century BC onwards. These preserved sources are also generally biased towards composed literature such as poetry, plays, histories, biographies etc. By contrast, many of these other surviving bodies of literature are less dense on these sorts of compositions but provide far more evidence of ordinary undergoings and daily minutiae. Likewise, we only consistently have Greek sources in any number from the 6th century BC onwards.

So we have a combination of things; many cultures that did have extensive documentation have had most of those sources lost, because papyrus and parchment do not tend to survive without intervention. Egypt is a very strong exception to this rule, because of its low water table and arid conditions for papyrus to be preserved in. If you imagine that many cultures kept records as extensively as the Egyptians, and that many of them happened to be in places where their writing rarely survived... In addition to that, westerners tend also not to be familiar with the surviving body of sources available for cultures outside Rome and Greece, even those those bodies of sources are at times actually larger and more complete. You'd also expect a lot of records to vanish over time, as front line state archives have always only preserved those records still relevant to the current functioning- it doesn't benefit them to keep somebody's tax records from 200 years ago. So in general our source material, across all of these cultures, comes from a combination of things; those specific pieces of literature somebody valued enough to copy out, or those that happened to survive at the time that the relevant archive was destroyed/abandoned/stopped working.