Lately I've been interested in the pyramids and how they evolved from simple mastabas put on each other into more complex buildings like the Bent Pyramid, and of course, the Great Pyramid of Giza, and then how they stopped building true pyramids when the power of the Old Kingdom collapsed.
However, what strucks me that there were seemingly no attempt to surpass the height and grandiosity of Khufu's pyramid. Considering that during the almost 4000 years between its completition and the building of the Lincoln Cathedral, there were several empires, rulers and emperors of whom many were just as ambitious as the pharaohs were, I'm surprised to see that noone even tried to build something more impressive than these ancient wonders. Or were there unsuccessful attempts?
Both the Great Pyramid of Cholula and the Sun Pyramid at Teotihuacan (possibly even the Huaca del Sol) are larger than the Great Pyramid at Giza, but only by volume rather than height. Not that any of these people were attempting to build a larger structure because they knew about the Egyptian pyramids. I'm just pointing out that larger structures do exist.
The Great Lighthouse at Alexandria also known as the Pharos was described as being 300 cubits tall. This places the height somewhere between 350 and 600 feet tall as the cubit can vary in length. This might have exceeded the height of the great pyramid which is 455'. Also the spire of St Paul's Cathedral in London was completed in 1240 Conservative estimates place the height at 460' though it is traditionally reported as 489' making it briefly the tallest building in the World before Being surpassed by the Lincoln Cathedral. The Yongning Pagoda in China built in 550 AD is estimated by some to have been 147m or 483 feet high which would make it the tallest in the world for a time If it didn't exceed the height of the Great Pyramid it was certainly close.
It should also be remembered that impressive can mean many more things than just tall. The Great Wall The Roman Aqueducts and many other structures are impressive though not particularly tall. Sometimes beauty and practicality are more important to the impressiveness of a structure than height.
Are you asking whether someone intentionally wanted to build something in order to surpass the grandeur and size of the Great Pyramid or whether someone wanted to build something so large that it also happened to be larger than the Pyramid?
I think the question needs to be clarified. No one even tried to build something "more impressive" than those ancient wonders? Certainly they were impressive for their time, but what of the countless castles, chateaus, palaces, and cathedrals constructed in the thousands of years since? Are they not also as, if not more, impressive than the pyramids? The palace of Versailles is almost mind boggling in its scale and ornamentation.
I think the impressiveness of these structures always exists within the context of the peoples, periods, and geographies in which they were constructed. The pyramids are an amazing accomplishment for a near-prehistoric civilization. Were they constructed in 1600, would they still be particularly notable in comparison to other structures from that period?