Definitely this is true, especially in Western Mediterranean/Western Europe- However, if I was trying to make the same point I would use different dates.. I am probably making some mistakes below and definitely leaving out a number of important other civilizations too elsewhere that also deserve mention..
Someday we'll have a much better picture, especially now with the huge advances people are making in technologies like synthetic aperture radar, photogrammetry and 3D reconstruction which is yielding a lot of information about what covered the Earth in antiquity that is new!
The romans had sewage systems, running freshwater, multi story apartment buildings, etc. Then it all collapsed (politically), the library of Alexandria was burned and the clergymen took over... It took almost 2000 years before any city was comparable. After that it didn't take so long until people figured out how to build steam engines and flying machines. Imagine if the romans would have kept going. What's holding humanity back is mostly politics and human stupidity, not physics.
I agree with the general thought you're trying to express here but I don't think the Western Roman Empire had it in them to get off their asses because of the continued existence of slavery, which was why the Sack of Rome was successful. The lure of coercive labor is very powerful corrupting influence which undermines innovation. And now we are very much falling into a very similar trap, with so called "Mode Four" (which is based on the Middle Eastern 'kafala' system) a stealthy shift which we all need to be aware of is happening to have any hope to prevent it! In short, we need to stand up for the rights of workers to be treated equally and paid equally when they are in the same country especially, and prevent the race to the bottom in all things which is occurring, turning it into a race to the top again, somehow.
Also, the sciences, math, and human civilization existed before the Roman Empire in a great many places, contemporaneously with it and afterward. Also, in Western Mediterranean there was a similar long period of reversal between the fall of the Minoan Crete civilization after the explosion of the Theran volcano (Santorini) in approximately 1600 BC and the rise of the Greek city state around a thousand years later. So really in the West there were two millennium long reversions of civilization each totaling around a thousand years.
Cities in China at the time of Marco Polo rivaled anything else that had ever been seen in the world by a European. The population of China was also larger than that of the US today more than a thousand years ago.
Also, when Cortez arrived in the valley of Mexico he described the Aztec city there (underneath present day Mexico City which is still the largest city in the Western Hemisphere, I think)
Anyway the Aztec civilization he found there was described as incredibly rich and complex and was I think described in the historical record as the equal of any in Europe at the time.
Contrary to what many believe the sum total of New World, pre-columbian, non-Christian technology was quite substantial and left a very large mark on the world which largely has not been acknowledged. In addition to a wealth of domesticated plants which totally changed the way humans lived in the rest of the world, (making possible a substantial increase in human numbers in areas which previously had not supported them) they also had agricultural technology which revolutionized agriculture. the Aztecs for example, used woven mats covered with soil upon which they planted crops in great variety) that seem to have produced more yield per unit of space than anything we do now except for hydroponic gardening which is based on it. Plus it was sustainable, not requiring any inputs which were not renewable. Of course the whole system fell apart very rapidly after the arrival of the conquistadors and much of its legacy was destroyed before anybody thought to try to save it. The first Americans also gave the world potatoes, maize, and made agriculture aware of the need to rotate crops (nitrogen fixing)
I want to mention here the legacy of Native Americans view of the world and where they fit into it, as steweards of the Earth, obligated to not take any more from it than they needed and incredibly attuned to the world around them in a great many ways which we live ignorant of today) Also their version of democracy (superior to the Greek version in every respect) and throw out that if we are to leave Earth and travel to the stars, we should strive to transform our society to be much more part of Nature, and living in harmony with other living things and in stewardship of the planet rather than obsessed with 'dominating' Nature. This is an absolutely crucial change I suspect we will not survive long in space without making. A number of posters in this thread have expressed sentiments along the lines that if we don't treat our planet and the rest of all of us well, we wont be successful in space either, or don't deserve to control other planets - where we may meet embryonic societies of intelligent life at earlier stages than our own, just as this may have happened to us in the past. (and soon 'we' will also include our intelligent machines, who-if we don't make the mistake of reverting back to the worst kinds of coercive societies, may I hope become our friends as well as our 'children'.)
At that point the 'need' in economic terms for humanity to be hierarchical and 'work' will have long passed however, work will most certainly continue and be transformational and I suspect far more productive than today, freed as it may be of a lot of very destructive baggage.
So, I think we should think long and hard what we want the long term goals of humanity to be, what is the path which will bring out the best in people. As its our choice. We especially need to prevent the urge to try to lock the planet or nations into anything as we are seeing.
Honesty is the road forward, dishonesty the road back. And we could learn a lot from the first Americans about democracy and living in harmony with the planet and the other creatures that we share it with too.
We probably would have learned much more had Spain not been in the midst of its centuries-long Inquisition, and the UK and the rest of Europe in the grip of a inbred incestuous group of rigid monarchies that had endless wars with one another over what amounted to family quarrels and ruthlessly eliminated any talent it could not control.
So I think your main point totally right, as far as so called Western Civilization goes, the periods of time when it has not been deliberately handicapped - when there have not been these huge barriers to progress indeed have been short.