The why not is an easy one - spy satellites are put into orbits which cover the likely hotspots for their use, and changing those orbits lessens the useful life of the satellite fairly significantly.
Oh, and no one really wants to give away the true capabilities of their spy satellites...
Not true at all. Reconnaissance satellites are usually on very low near-polar orbits, completing an orbit in 60-90 minutes. As the Earth spins below, they cover the whole thing. However, the sensors onboard collect more data than the available bandwidth, so they do not transmit the data about uninteresting areas, such as over the open ocean where nothing of interest is expected to be.
You could make a point for storing a 48 hour buffer of all untransmitted data for later transmission if it is deemed necessary. However that has it's own set of problems, such as energy budget, cost and weight, and being susceptible to problems such as cosmic rays flipping bits.