The "may come in handy someday" element is good! However, it is probably good to use it sparingly and in a way that is memorable, more than an off the cuff explanation that will probably be forgotten. We didn't know the history of Bilbo's ring, after all, until it was important to the story. Likewise, there's no reason to tell the players the history of the sword until said history can affect the game.
As an example, say the PCs found the ancient sword wherever. Then, later, when traveling in the frozen northern village, the villagers recognize the sword, treating the PCs as honored guests, the NPCs telling the PCs about the whole pure heart thing and the tale of Fromir's death. Good stuff, and something the players will remember! Now you've ingrained the history of the item into the players much better than telling them, because they have concrete reason to appreciate the sword, as found in play.
Now, they can do all that stuff you want them to. Find out if their heart is pure, try and reunite the tribes using the sword as a banner, and if the descendant of the frost giant appears, they won't have to remember back to the two sentences you gave them four months ago offhandedly. They can look back on the time they were treated as heroes in that village while traveling through the harsh norther climes.
So, I'm not saying you shouldn't use history. I'm saying your approach to it is wrong. Or, at least, not as interesting as it could be. That way you get your cool history and the players are invested in it because they want to be. Because you invested their PCs. Not because they're playing nice with you. But, because its fun!