This is like comparing apples and oranges. I'm inclined to think that the creator of this video is biased towards AeroFS.
Really, no reason? None at all?
For "infinite versioning", it's obvious - there's no upper bound on the amount of data the server has to store. Storage space costs money.
As for no direct LAN syncing, someone's already mentioned the reason - consistency. Syncing is already a hard problem, and it's dangerous to allow more things to go wrong because the clients synced but the server didn't receive all the data.