I would guess if the capital and talent marshaled to send a man the the moon had been tasked to build a global mobile communications network we would now have a better Internet and would have had cell phones a decade earlier.
The difference with these and the space program was that the space program had a very specific goal. These, on the other hand, are technological exploits.
I.e. a "high-speed rail system" is not a goal in itself like the space program was but a goal of "smallest possible travel time with lowest cost between points A and B" would be. The end result of this might be a high-speed rail system, or something else entirely.
The value of programs with ambitious targets is that they will provide real world solutions forged out of necessity. Sometimes these will lead to new areas of industrial production, sometimes find that all they will need is a bunch of ducktape.
To make great leaps, we usually cannot put the technology before the end. It all starts with a great goal. Von Braun was obsessed with rocket engines because he wanted to explore the space. Heisenberg did not invent linear algebra (he was not aware it already existed, I think) because he was obsessed of numbers but because there was a specific physics problem he wanted to solve and he intuitively grasped he needed new tools to calculate the stuff he needed to calculate. Etc.
The real world problems provide two things at the same time: need and validation. They create a real world need, and if the new technique provides a valuable solution, it establishes the usage of this technology as a valid method.
