You are just seeing an artifact of memory. Aside from the fact that we have much more information-recording capability than existed in the past, when people talk about "important events" at a distance they are usually filtering out things that they have decided are "unimportant" based on later events. But when you are living through something, you don't know what is going to be important or unimportant later on.

A favorite example of mine: on the morning of August 7, 1945, many major newspapers carried two large headlines. One was the bombing of Hiroshima. The other was the death of Major Dick Bong. You have probably heard of one of these events, and consider it to be important. The other event is probably so obscure to you that you might for a moment think I am making up the name "Major Dick Bong" and saying that it was treated of sort of co-equal importance with Hiroshima. And to be sure, even at its most, the death of Major Bong was in a somewhat smaller typeface than Hiroshima. But it was still a pretty big announcement — it was important news of the day according to the people.

Major Bong was an important military ace and test pilot that many people had heard stories about, so his death at age 24 was news people cared about. But over time, Hiroshima has become cemented as a major turning point in modern history, while Major Bong's death was just one of an almost uncountable number during the war. And so Major Bong swiftly got demoted to a minor event, whereas Hiroshima was the major one.

If you read any old newspaper, you'll find lots of "major events" that nobody today cares much about, because they didn't add up to much later. Hiroshima stayed a major event because it became a symbol of an entirely changed world. Major Bong's death did not.

If you dive into any moment in history where we have any significant records, you will find it just as diverse, momentous, and complicated as anything today. There is a trilogy of books I've enjoyed written by a group of authors called The Mongoliad, and it is a heavily fictionalized description of events leading up to and after the death of Ögedei Khan in 1241. Now I am not one who is much of expert of the 13th century; as a modernist, there 10th through 15th centuries are sort of a big blur to me (e.g., between the fall of Rome and the discover of the New World), even though I know a lot of things happened then.

But the real genius of the book is that by focusing in a deep way on the world of 1241, they really illustrate how much is going on in the world. There's almost too much to keep track of when you start going over it. Because that world was never as "flat" and "boring" and "lacking history" as you might imagine it to be — that's mostly an artifact of ignorance.

Now, some of this also depends on how you define "history." E.g., if you define it by technology, the rate of technological development has definitely changed over time. There are reasons for that — technological development is a cultural product and different cultures have had different conditions for its development. Similarly what we might label as scientific discoveries. But if you look at "history" more broadly, and include all human activity under that, you'll find that at no moment were people just sitting around doing nothing. They were constantly doing something, though what that something might be could vary by society quite dramatically. This is even true of pre-history, which we tend to abstract even more ("tribes and hunter-gatherers," as if they were all the same and did nothing to distinguish themselves for hundreds of thousands of years), even though the archaeological record points to tremendous cultural innovation and change.

The only plausible argument you could imagine making for history "accelerating" is that the number of people has dramatically increased in the world over time. In 1500, the world had maybe 500 million people living in it. Today it has almost 8 billion — an increase by a factor of sixteen or so. What implication does that have? Well, people are the engines of history: they are the ones who make your discoveries and wage your wars and make your art and debate their ideas and so on. So there is an argument that some aspects of history are going to necessarily increase in the rate and complexity the more people there are; this is one argument for why science became so much more of a force over time, because there were just that many more people doing it.

This argument is interesting though it is pretty crude in many ways. Having lots of people does not guarantee you will make more discoveries by itself; if that was the case, China and India should have dominated the world of science almost since it existed, and many of the most innovative nations became that way because, in part, of their populations being smaller than others (e.g., Europe's push towards mechanization of labor was in part a result of their labor costs being much higher than countries where populations were high and thus labor was cheap; said mechanization of labor is more or less what kicked off the Industrial Revolution). Structural conditions matter, "culture" (broadly speaking) matters, resources matter, and so on. But that doesn't mean that population doesn't have some impact on all of the above, either as a stressor or a contributor or a "pool" for various things (scientists, soldiers, laborers, etc.), and it is something that one can definitely, quantitatively say "increased" over time, unlike most other variables one might measure.

But by and large I think the answer is to be found in a combination of selective records, a definition of what both we and people in the past deemed to be "important" enough to put into records and histories, and the pruning that happens as one decides over time that some things were indeed very important, but some things (poor Major Bong) were less so.