Size equals speed. You'll find out a lot more a lot quicker about how to fling things into space if you try flinging something big with people in it than you will with small(er) satellites.
Then there's the issue of resources. A small, lower profile project will drown in the midst of others. A big, high profile one pushing the boundaries, on the other hand, is bound to draw in the very best human resources. And when you put the brains together, it will lead to all sorts of new discoveries and inventions.
Thirdly, most of the discoveries and inventions from project X will have no use in project X, but will find use elsewhere. Again, the bigger and more complex the project, the more inventions you get.
And lastly, the knowledge gained from the moon landing project was indeed absolutely crucial to satellite communications( and a zillion other things).
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