Why is the Prologue to The Canterbury Tales a story for all ages? How do three characters illustrate this? What does it say about human nature?

The Prologue to The Canterbury Tales is, indeed, a story for all ages.
Using the Prologue to include what is known as "estate satire," Chaucer ridicules the abuses of the three traditional estates, the major social classes composed of the clergy, the nobility, and the peasantry. Chaucer satirizes the vanity and greed of the clergy and intellectuals. Also, Chaucer parodies himself with a character named "Geffrey," who is a weak storyteller. With this character, Chaucer generates a playful and light-hearted tone.
While these classes of people are characteristic of Chaucer's time, his pilgrims are yet representative of types found throughout time and in modern society.
The Friar
The Friar is a charlatan. Professing to be a humble servant of God who has taken certain vows, the Friar is instead "a sportive man, and merry" (208), who loves gossip. He hears confessions, but if he knows he will receive gifts, his absolutions for the sins of the penitent are "soft and pleasant" (222). He also stuffs his cape with "generous presents" for pretty wives when he sees them. In short, wherever he can best serve his own interests, the Friar makes an appearance.
This conduct of the Friar is not unlike that of some of the more infamous television evangelists in contemporary times (e.g. Jim Bakker and Jimmy Swaggart).
The Squire
Another character whose personality we see throughout the ages is the Squire. While his father, the Knight, is not home long from one battle before he enters into a new battle (he is a "worthy" man who holds "chivalry in his heart, and honor and truth, and courtesy" [46-47]), the Squire is a professional soldier only because of the attention he receives from the ladies:

He'd ridden with his father, on cavlry raidsIn Flanders, Artois, and Picardy, and madeHimself useful, working hard to build a nameAnd have his lady think him already famous. (85-88)

This attitude is not unlike men who join the Armed Services because there are women who are easily infatuated by men in uniform that seem handsome and brave.
The Doctor
The "perfect practicing physician," the doctor seems to know the cause of every malady. He immediately gives the patient his medicine because all his apothecaries are ready to provide what he needs. "And each made money from the other's guile" (426).
This collusion between the physician and the apothecaries is not unique to Chaucer's time since greed has always existed. In the US, for instance, a law was passed in 2013 that requires all pharmaceutical companies to disclose their payments to doctors.
Certainly, then, Geoffrey Chaucer's Prologue from The Canterbury Tales depicts many universal human traits, making it a tale for all ages.