He was leading all-hands meetings by having the teams shout "Domination!"[0][1] He's always been obsessed with Roman Emperors too, particularly Augustus (though as a Romanophile myself, I relate). Kara Swisher mentions this a lot. Even in his early days he was the "alpha nerd." Dude is obsessed with power and always has been. He explicitly cultivates this image of being above it all and just wanting to connect the world, but if you watch Facebook/Zuckerberg's actions they're always about expanding power. Similarly, Augustus PR was legendary enough to found a dynasty. He never called himself an Emperor, just the "first citizen", a citizen like everyone else, and he only was the "first" one to provide peace and stability to the people.[2] He only acquires personal power at all costs for you. Also, Zuckerberg builds shadow profiles of everyone that ever browses a website that has a facebook 'Like' button on it because it and will never delete your data because he's creating a connected global utopia.
[0] https://www.wired.com/2012/05/network-effects-and-global-dom...
[1] https://www.vox.com/first-person/2018/4/11/17221344/mark-zuc...
At this point, Facebook isn't even about Facebook. Facebook is a typical giant that acquires other companies. I would argue WhatsApp has more impact on the world than Facebook. Zuckerberg can't be proud of WhatsApp though, since he didn't build it.
To me, there is clearly no higher purpose here besides power.