There is only about one scenario where i would see it possibly properly in use.
(likely what I will do when I switch to bridge mode).
I currently have smart home monitoring, with the seperate Netgear router.
Its currently plugged into the CGN3 in NON bridge mode.
My modem is in the basement, My router (even when i switch to bridge) will be upstairs, and dont want BOTH wireless right beside each other (for lessening interfearance, even though on different channels).
What i would likely try then..
Is leaving the port one running up to my ASUS. Then in the 2nd port, the netgear.
It can get a seperate external IP, etc. It doesnt have to have any other communication to the rest of my existing network, etc.
A second IP address could be usefull if you wanted to run the Home Monitoring on its own network as Gdkitty indicated, or if you wanted to use a separate VPN service and not have it interfere with the rest of your home network. Or you could use one network with Open DNS and another network with the Family Open DNS address which filters IP addresses for kids. There are probably other uses that are possible that don't come to mind at the moment.
The big question is whether or not the modem will be stable in Bridge mode with two networks running their own IP addresses.
I am using the 2nd IP with my Linksys VoIP adapter since it is also a NAT router I was not concerned with securing it behind my firewall. This way I do not need to mess around with port forwarding on my firewall and I can tinker/upgrade etc my firewall while keeping the phone running.
Sorry should have mentioned i have an older CGN3 with no issues with stability using the second address. Doesnt really help the original poster...was just adding another use case for 2 ip's.