Monuments have been erected to historic figures throughout for as long as artists have been able to paint a picture or sculpt a figure. But today we have a problem with creating monuments to our national heroes, first because of a lack of artistic talent both in architecture and in sculpture, but also because of a lack of understanding of that a monument is a work not of history, but of poetry.
In Aristotle's Poetics (which I keep a heavily noted and worn copy on my desk) he distinguishes between poetry and history by telling us that history speaks of "what actually occurred" but poetry speaks of "things which are likely to occur." He then makes the claim that because of this, poetry is more universal than history. History gets caught in the details, the particulars of actual events, but poetry, speaks only of what most likely happen.
Another interpretation would be that history deals only with the actual acts of a man, but poetry is more likely to show the true character. If one is more concerned with the actual historic truth of Napoleon, we would never show him in painting or sculpture towering his adversaries, as he actually was diminutive in stature. Michelangelo, when sculpting an image of a scion of the Medici was told "that looks nothing like him," responded that "in a generation no one will know." Historically he sculpted a false image, but to poetry he sculpted the man so that his inner virtues, his magnificence, power, etc, were expressed through his physical form.
Today in sculpture and in monumental architecture we have a problem expressing historic figures poetically. Part of the blame could be laid at the foot of photography, as we no longer have the artist as intermediary, but then again, sculpture and painting still were expressive well into the 20th Century.
The problem lays with our understanding of history, that we obsess over the details of a particular person's life rather than expressing the universal virtues which he possessed. No monument today it seems is complete without an expansive "interpretive center" or museum to tell us the every tawdry detail of the subject's life. We even go so far as to emphasize the vices and physical ailments of our subject. A modern monument becomes so obsessed with telling the "facts" that it fails to tell "truths." History is the telling of what was, but poetry is a telling of what is and what ought to be, and thus is how a historic figure can be alive and meaningful despite being long dead.