Yes, I also wonder why embassies have to be on homeworlds only. It may make sense when compared to real-life politics, but I think it would be much more useful for the game if you could establish an embassy or some kind of outpost on all enemy planets. These outposts would be a kind of a civil starbase with upgrades like permanent planet vision, slowing of trade, production or culture spread, stealing income and so on. Maybe you could make them immune to weapons fire (diplomatic immunity blah blah), making the only way to remove them a "expel diplomat" option that your enemy has to research and that woud cost him money when he uses it.
Maybe such outposts/starbases could be placed on all enemy planets, while an embassy would still have to be built on homeworlds. Embassies on homeworlds could give global benefits that affect the whole enemy empire like slowing their research, giving you positions of all enemy envoy cruisers and so on.