I would argue that it's a better world because Americans spent all that money. Those billion dollar rockets are how we learned to utilize space. In the process, we built gps, satellite communications, digital cameras and countless other technologies that the world enjoys today.

Without the space program we would never have had super soakers, and frankly, I didn't want to live in a world like that.

*Super soakers were invented by a NASA engineer. It's not hard to see how much a super soaker has in common with the fuel injection system for a pressure fed rocket, they're essentially the same thing.

All that said, you're not entirely wrong, throwing away rockets is a bit crazy. But we've come a long way in the field of reusable rockets. Within 3 years, I expect we will be putting a whole lot more in orbit at a much lower cost, because fully reusable rockets are nearly here.

I'm not sure it would have been possible. The amount of computing power to land a rocket like that is insane.

In order to land in other ways, the rocket has to be really small (parachutes) or have too much weight consumed by an airframe (space shuttle).

It probably wouldn't have been possible to get to the moon with the restrictions those designs would have imposed.