How does the story of Romulus relate to the rise and fall of Rome?

The legend of Romulus and Remus relates only to the foundation of Rome.

Romulus and Remus were the twin sons of Rhea Silvia, the daughter of Numitor, the king of the Latin city of Alba Longa who had been deposed by Amulius, his brother. Amulius forced her to become a priestess of Vesta because these priestesses had to vow chastity. This meant that she would not have children who could challenge him for the throne. However, Rhea Silvia had two sons and claimed she was impregnated by the god Mars. Amulius arranged for the twins to be put in a basket and thrown in the river Tiber. The twins landed by the Palatine Hill, in the area which was to become Rome. They were breastfed by a she-wolf and then adopted by a shepherd, Faustulus, and his wife, Acca Larentia.

When the twins grew up they learnt what happened in Alga Longa, deposed Amulius and restored Numitor. The then decided to found a new city in the area of the Palatine Hill. There was disagreement. Romulus wanted to found the city on the Palatine Hill and Remus on the nearby Aventine Hill. They decided to resolve the dispute by Augury (a divination which read the omens of the gods). Romulus won and then begun to build a sacred wall around the Palatine Hill. A spiteful Remus trespassed the wall and Romulus killed him.

The actual foundations of Rome din not involve the building of a new city. It was the unification of separate settlements on what were to become the Seven Hills of Rome (the Palatine, Aventine, Caelian, Esquiline, Viminal, Quirinal and Capitoline) into a single state ruled by Romulus. The earliest evidence of human settlement in the area of Rome dates to the 14th-13th century BC. That is, 500-600 years before the date of the foundation of Rome (573 BC).