Once the ball has traveled ten yards it's 'live' for both the receiving and kicking teams as long as it remains in the field of play.

If a kickoff is fielded in the end zone, the receiver can choose to run it out, suggesting that the end zone is part of the 'field of play'.

But if a kickoff lands and dies in the end zone, officials will whistle for a touchback without the ball having been fielded. If that ball died on 1-yard line it would be up for grabs. Why does the receiver not have to field the ball that dies in the end zone? Why could the kicking team (in theory) not recover that ball for a touchdown?

Not that it would be likely to ever happen, but I watched the opening kickoff in today's Denver/New England game land, and stop, in the end zone and then blown dead with no touch from either team. I immediately wondered why that was since I thought the end zone was part of the field of play.