I never understood the aliens as harvesters as a threat movie plot / Hawking logic. There is SO much stuff in space. All of the stuff. Why care about our stuff? Intergalactic highway imminent domain? Just chart a different course. There’s no reason other than to mess with us for fun like dolphins jacking with a pufferfish. I guess maybe I’ve stumbled onto a sci-fi short story idea.
I think the biological information on earth would likely be extremely valuable. Our DNA took an absurdly long time to evolve, and would probably be almost impossible to acquire with simulations given it spans from microscopic to macroscopic factors. Works of artistic or cultural significance probably have a decent chance as well, given the value we place on those even from ancient or foreign cultures. Whether our biosphere/temperate planet has value probably depends a lot on your assumptions about how hard terraforming is for super-civilizations and how compatible life is.
On the other hand I agree our natural resources are likely worthless. I always laugh at that scientology movie, Battlefield Earth, where the aliens invade, then inslave humans to dig in Earth's gold mines with pickaxes. Maybe the most troublesome possible way you could acquire gold as a spacefairing race.
As a hobby project I'm making a video game about aliens looting museums and zoos for items of cultural and biological value. Mostly because I find the idea of little green men busting up the Louvre then blasting off to be very funny. The zoo angle is a little nonsensical if you consider how much DNA is shared, but obviously scooping up pondscum is a less interesting scenario.
Sometimes we do, or to avoid all kinds of specially designated species. There are reams of complaints throughout construction history about being unlucky enough for your bright new infrastructure project to be heading right for some politically or socially de jour habitat that activists decide they want to protect.
Who's to say that there doesn't exist a cosmic version of Greenpeace that has been actively pamphleteering some galactic government into not star-lasering(1) our little green and blue anthill to a husk for its latest celestial mega-infrastructure project?
