Ludicrous. If everyone could see everyone in the world, then there would be no corruption due to secrets. Now how do we relax that to reality. 
No, that's not so unreasonable. It's not true, of course, it's an assumption, but in a highly connected network the broadcasts are quite reliable. You can try to amuse yourself by computing the probability of a message being not received by a peer when everyone is connected to N other peers, as a function of reliability of a connection and size of the network. Imagine that everyone passes the message to all neighbors once upon receiving it.Now with not-always-online nodes there may be problems, but again these could be addressed to minimize damage to them.
The point I was making by analogy (was not about the viability of propagating the info to those who are online rather) is the "always-online" is about as far from reality as you can get. There is no way to relax from those who are always online to those who are not always-online being able to know who to believe is telling the truth.