1. There should be a bonus starbase per 200 or 300 sprawl. (Not too much but not nnothing either)
Maybe as a replacement for the current system.
2. Large empires are intimidating, needs a bonus of diplomatic weight, per sprawl point. 1% per 100? 200?
The things that got you that sprawl are mostly increasing your diplomatic weight, there is no need to doubble dip.
3. If I'm so sprawly, surely I have more space to store stuff! +1000 resource storage per 100 sprawl?
I'd like to have more passive storage capacity, I don't want to hook it up to sprawl
4. Vassals/members fear me (as suggested on the main thread by someone else): reduces relation penalties by x% 1 per 200?
Countersuggestion: empire sprawl increases the threat generated by your empire (if it doesn't already). If I've conquered half the galaxy the other empires should be more worried about me than their interpersonal rivalries.
5. Sprawly empires have greater reach! Reduces range penatlies for relations,treaties, or even starting federations (that one is soo anoying currently)
The exact opposite of what sprawl should be doing, taller empires should be making up for their lack of size by forming relationships with whoever they can, wide empires already can reduce those range penalties, by reducing the range (conquest)
6. Network effect! : Trading bonus due to internal synergies within the pops/planets/systems of the empire: +1% trade value on each planet, per 100 sprawl.
Same issue as the last point, wide empire doesn't need to squeeze their pops for value tall does.
7. Reduced influence costs due to distance: -3 influence cost increase per jump, per 200.
An interesting thought, maybe with a civic or AP (Interstellar Dominion comes to mind) not with sprawl.
Encryption penalty, the more pops you have of diverse locations, ethics, and ethnics, the easier it is to spy on you.
Influence cost of friendship, the bigger you are the less friendly you look, the harder it is to convince others your a good friend, the more your factions need to be convinced it's a good idea. Won't really apply until an empire gets a higher proportion of all the sprawl in the galaxy.