[Formendacil]

Tolkien doesn't directly say--at least, that I can recall--why the Grey Company was important, if indeed it was, but I think there's a symbolism to it that makes a lot of sense in Middle-earth AND explains why it was dropped from the movies.

Basically, the Grey Company transforms Aragorn from a lone hero to a lord. Before they show up, he's a hero, certainly, and kingly--but other than lineage and his person, he's not a king-candidate: and his arc over Books III & V is becoming one.

The arrival of his people fits that point excellently because they arrive right before he challenges Sauron in the palantír: so as he marches to war thereafter, he's marching with at least a token force that says "here is the King of Arnor; here is the Heir of Isildur."

But Sauron's not the only audience: he's also bolstering his lordliness to the people of Gondor. When he arrives like the wind to Pelargir, he's not just a hero leading the army of the dead, he's a leader of men marshalling the army of the dead. The fact that he has a retinue is important (though it's implicit not explicit) in winning the respect of Angbor and the other southern Gondorians: here are people to vouch for him and his lineage.

The idea that a king is just a prince who's the heir to the last king doesn't quite fly--historically, an heir too young to be a leader in his own right (a child) was always a dicey prospect to succeed. If you look at Faramir, he's already "the Captain" and has his own band of men--it's not just that he's Denethor's son. (This is presumably true of Boromir as well, but we don't get to see it in the firsthand narrative.)

But this is always why the Grey Company is dropped so easily from the movies: because Peter Jackson's Aragorn is a hero, not a lord, and his arc isn't the same as Aragorn's more carefully-laid triumpt in the Books. Movie-Aragorn sort of falls into becoming king reluctantly, while book-Aragorn has worked uphill to accomplish a mightly goal: the Dúnedain arriving and marching with him are a step toward that goal. Without them, he'd just be a man with a sword; with them, he's the Heir of Isildur. Even then, it takes the Army of the Dead and impeccable timing at the Pelennor, and the semi-related suicide of Denethor to let everything slot in for his becoming king.