Fair enough. Why do you think Rowling even bothered to foreshadow House Unity?

 

Because one of the biggest theme of the Harry Potter Series is actually overcoming bigotry and prejudice?

• Blood Purity vs. Muggleborn
• House Elves enslavement
• Centaur Prejudice
• Slytherin Prejudice
• Goblin Prejudice
• Etc.

Some of them were overcome through the Series by Harry (Slytherin), some by society (Blood Purity kinda, still WiP I guess), others were not. The Sorting Hat was only another voice adding its own weight to the fight. I see no particular reason to pay it more attention than any other. After all, it's not like the hat has the foresight. It just encouraged House Unity, probably out of duty to the memory of the Founders who once worked together to build the school. School which the hat probably doesn't want to see altered or destroyed by the evil lord Voldemort.

Now, why did Rowling use that? I'd wager that she had to write another song for the Hat and wanted it to be different than the first one (and only one) Harry heard. Tie it with the global conflict of the book and you give it even more importance in the narrative.

 

Actually, this is kind of an important point. I don't think foreshadowing was the right word, it's more of a warning:

In other words, it's not saying, "House unity is definitely going to happen!" It's saying, "If house unity doesn't happen, shit goes wack, yo."

I think we can all agree that the house unity was at best imperfect, and so what happened? Dumbledore died, Voldemort took over the school, and a huge battle was fought on Hogwarts grounds. Yes, the good side won in the end, but at the cost of many Hogwarts students' lives, and presumably at least a few teachers as well. And the reason this all got so bad was because the divided student populace was unable to properly resist the "external, deadly foes", with many students even supporting the Death Eaters.

And it doesn't really take precognition to tell all that. The hat explicitly says:

He's just basing this off of stuff he's seen in the past.