Why did the lightning network implement a gossip protocol?
The main idea of Lightening Network is to make the Transactions as fast as possible and to solve blockchain Network scalability issues. Whereas the main essence of the Gossip protocol is that each participant randomly selects a peer and exchanges state. As it can be seen that  Gossip approach is converging in O(logN) gossip rounds where N is the number of participants. Whereas communication on off-chain Network is only O(1) hence reducing the space on the blockchain. Applying Gossip protocol to the lightening Network on defeats the property of 'Lightening' and makes the network massively less scalable. Hope you like the answer.