This makes power generation a bit more challenging.

There are sun synchronous orbits (and the orbit at the dawn/dusk terminator is an interesting one - https://en.wikipedia.org/wiki/Sun-synchronous_orbit ), but there isn't an easy orbit around the Earth such that it is always in shadow... or rather, that's the Earth/Sun L2 point... which is where the JWST is. At that distance you lose the magnetic shielding of the Earth (and makes it even more expensive to get materials to and from it).