Not to know what happened before you were born is to be a child forever. For what is the time of a man, except it be interwoven with that memory of ancient things of a superior age?
Marcus Tullius Cicero, who was assassinated 2052 years ago today, wrote this. It seems to me that nowadays ancient Rome is more a myth than reality for most people. It takes a conscious effort to think of Caesar, Mark Anthony, Brutus, Octavian and Cicero and remember that they were real people.
I grieve for the Roman Republic. What splendour could we have achieved today if the republic hadn’t ended?
I think we would already be on Mars. Have colonies on other worlds. Giant space stations. Medical and scientific knowledge beyond our wildest dreams.
I wish I had known him and his contemporaries. These must have been fascinating times.
Verena Kyratzes 
The Enlightenment modeled itself pretty much on antiquity, that’s including Rome, so that should answer your question. As for freedom and equality:
There are historical records that mention Senate discussions on such subjects as the abolition of slavery and female suffrage. None of these proposed laws were passed but the discussions continued. And remember that in modern times these processes also took a while. And although women were technically forbidden by law to partake in political discussions several speeches by the known arch-conservative Cato survive in which he calls for these laws to be actually enforced. So we may assume that women did dabble quite a bit in politics back then.
I will grant you that the Romans seemed to have a “problem” with defining who was a Roman citizen and who wasn’t and following from that which rights were available to you, but then again that also was under almost constant discussion and the legal boundaries of Rome were frequently enlarged.
So, yes, Rome definitely was a lot more civilized and enlightened than anything the Middle Ages produced. And they were closer to granting women suffrage than most European countries were in the beginning of the 20th century.
And yes, alternate history sounds pretty good right now.
What about Enlightenment ideals? Freedom, equality of status and opportunity, the rule of reason, one for all and all of that? Did ancient Rome have analogues of that, or could they develop them in time?
If they did, I am so rooting for alternate history.
It’s not only that. Every time I try to talk to someone about roman times they get this vacant expression, like I’m trying to talk to them about a fairy tale or a fantasy book. If it’s a woman that’s usually five seconds before she gets started about women’s rights in the ancient world. (Right… women in Rome where entiteled to get divorced and obtain very important religious offices. Try saying the same for the Middle Ages.)
Shakespeare’s “Julius Caesar” doesn’t help us, does it? To remember that they were real people.
I think your point is valid. How much of history has the human race squandered? The answer is… an awful lot.