A current theory is that it contains the Philosophers stone, its certainly more important than just a rock.

It's certainly not the Philosopher's Stone. The only reason the stone isn't at the Ministry (or Gringotts) is that Hogwarts provides the absolutely best protection:

"I do not own it, that thing which Voldemort desires. It belongs to another, and is held here by his consent! I asked if it could be kept in the Department of Mysteries. But he would not permit that—he said it must be within the wards of Hogwarts, in the place of the Founders' protection—" Dumbledore passed his hand across his forehead. "No," the old wizard said in a quieter voice. "I cannot pass this blame to him. He is right. There is too much power in that thing, too much that men desire. I agreed that the trap should be laid behind the wards of Hogwarts, in the place of my own power" (Ch 79).

I can't see Dumbledore going and giving it to Harry to wear on his finger.