Diplomacy needs an overhaul. Even with ethics it's quite barren and showcases little in the way of empire personality. There is so much tied up here that remains unexplored: trade, espionage, warfare, or even a galactic council attempting to impose its will. Currently, too much information is immediately shared when you encounter a new empire for the first time, especially regarding military strength. For instance, as a xenophobe, I should be able to keep what's going on in my space a secret, unless infiltrated.
What purge? These are baseless accusations fabricated to smear our empire! You have no proof. Humans are a myth; they never existed!
I'd also really like to see the development of more internal empire mechanics, especially those related to primitives and their integration. Sure, there are a few events that let you tool around with their ethics, but they are tacked on and random. Enlightening (or enslaving) a species from the bronze age should allow us to customize their traits or development in more detail. Modern civilizations, on the other hand, might prove more unwilling to assimilate into a society they abhor. The addition of species rights in the upcoming patch is heading in the right direction.
Lastly, it seems like Stellaris could benefit from "galactic wonders" aside from sheer technological superiority. Maybe a species could be the first to build a universal translator and receive diplomatic or espionage bonuses? The founder of the galactic council receives a permanent seat or an additional vote? Constructing an interstellar stock exchange allows an empire to heavily sanction a rival or corner the energy market? This would give us practical methods of domination other than war and might be useful for a species trying to play tall. How such projects would be unlocked, built, and integrated into the game's interface is open to discussion.