Of course there's no reason why we need to build the collector at the Earth's orbit: the closer we get to the Sun the smaller we can make it. The linear size of our structure goes down directly with the distance from the Sun. If we go into about Mercury's radius we can only need about 100 square kilometers or a square 10 km on a side.
So we need only very modest structures to collect solar power and since it's already in the form of electromagnetic radiation we can build mirrors to concentrate and direct it where we want.
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