Benefits to private networks between virtual machines on an ESXi host?

Solution 1:

Private networks in a virtualized environment are not for providing redundancy. The advantage of private networks is that you can separate backend traffic from frontend traffic (e.g. traffic generated by users accessing a service). You would put only the frontend servers on the public network and connect frontend and backend servers via a private network. That removes one attack vector (direct access) from your backend servers, because an attacker would have to go through the frontend server(s) to be able to access the backend servers. If the private network uses a separate set of physical interfaces, you can also prevent frontend traffic from exhausting bandwidth of backend connections.