Why the ending is significant

The very fact that the two lovers do not wind up together is very important to the movie, in looking at it from this point of view, you come to the realization that the events in the movie- that one day, is the most special day in the lives of both of those people. The day and the events therein that they go over again and again in their memories like the page in a beloved book that holds their favorite poem, the one she thought was by Keats and the one he insisted was Shelly. Set apart from the routine and boredom of day to day existence
If they had gotten together, and Married, in the very Hollywood way, then that day would only have significance as the day they met.
Since they soon parted, we assume to never see each other again, the memories of each other will remain unstained by the troubles of life, they will remain, all of them as perfectly beautiful as they themselves were those many years ago, when they were both young and beautiful in the eternal city of man. And this movie becomes a perfect crystallization of that special day when two perfectly fitted people met each other and soon lost each other, not for want of anything but the obligations held by one to millions of strangers., royal subjects, who in the end, care very little for the person, but care a great deal for the title.
It is also significant that neither character is Italian, and Rome is not the city in which they will live out their lives, but Rome will always loom large in their memories, as that special place of good fortune, that dream scape of their most favorite thoughts. Their special place, the place of their youth and happiness.
As the audience leaves the theatre they are very much like the two star crossed lovers they have just witnessed on screen, happy to have made their exquisite company, but strangely sad at how it all worked out.