Speaking very generally (and based on slightly faded memory), one reason they liked old things in the Renaissance was because there was a point of view that the prior ~1,000 years, since the fall of Rome, was a waste intellectually, and that the way forward was to revive the Roman and Greek knowledge. I don't think the same conditions apply today, and IMHO perhaps Humanism's goals should be accomplished by other means than focusing on preserving or reviving the past.
(Disclaimer: The following mostly is based on memory; details may be off a bit. Sorry.)
Hegel said in the 19th century (paraphrased), "he would 'put on seven-league boots' in order to skip over the thousand years between the 6th and 17th centuries and, having at last arrived at René Descartes, said that now he could 'cry land like the sailor.'"[0]
Even the name of that prior, wasted period, the "Middle Ages", was given to it by people in the Enlightenment: From their point of view it was the middle between two great periods: Classical antiquity of Greece and Rome, and the Enlightenment.
The Middle Ages ended, in a sense, with the reintroduction of most of the ancient Greek philosopher Aristotle's works to Europe, where they had been lost for centuries. Aristotle was highly respected and presented a worldview that challenged Scholasticism, the philosophy of the Church. Thomas Aquinas, a name many recognize, made it a mission to reconcile Aristotle with the Church.
It's a good reminder that civilization is a fragile thing, and we are stewards of it. We don't want the next 1,000 years to be lost, too.
[0] https://www.britannica.com/topic/Scholasticism