I think you answered your own question in the first part: Gossip at no-cost on a broadcast network is a potential Denial-of-Service attack vector. Since there is nothing stopping Sybil from creating many nodes and false channels, she could easily overwhelm other nodes who receive and rebroadcast gossip.
Since gossip is rebroadcast without reward, the incentive to engage in gossip is so that your own node has a robust, up-to-date understanding of the current state of the network which will improve the probability of your payments succeeding, and provide you with more routing options which may reduce costs.
But gossip must ultimately be limited in scale. It will not be possible for billions people around the world to globally broadcast channel states every 2 weeks because most people will not have the bandwidth or computers powerful enough to process gossip of this scale.
Having an up-front cost to channel creation - the requirement to broadcast a 2-of-2 transaction on the bitcoin mainnet, is an extremely useful way of mitigating the DoS vector, as any potential attacker must expend real bitcoin in transaction fees in order to create many channels.
There are other proposals to limit the scale of gossip by reducing the requirements each node must have, and offloading route-making decisions to others. These have trade-offs in privacy, reliability and censorship-resistance, and some may create a centralizing effect which could end up with a hierarchy of registrants in a system like DNS.
So if anything, the goal should be to continue to make efforts to reduce or constrain gossip requirements, and ensure that there is always a tangible cost to advertize a channel.
Communicating false channels should be done over an alternative gossip network which might have a different incentive mechanism in place to reduce the DoS vector - but I suspect attempts at this will lead to a centralized registration network like DNS.