So we now know what Homeworld is dying and dwindling on resources. So this begs the question as to why they don't just colonize some other planet? Why not Mars? Or Mercury? Or the Moon? They built a base there.
Well, we have to look at what Homeworld harvests: they gather gems, which means the atmosphere and the conditions for gems to exist must be perfect. They can't mine the Moon and get the same gemstones, if any. They need a live ecosystem to harvest and mine from. And there are very few planets that hold these conditions, and Earth is one of the few.
This one was short but many people seem to skim over this.
"We all want progress, but if you're on the wrong road, progress means doing an about-turn and walking back to the right road; in that case, the man who turns back soonest is the most progressive." ~CS Lewis