LAN IPs are also useful for distinguishing computers from the same external IP which could help compromise your identity or privacy.
And I'm fairly sure my Sys Admin won't want random websites knowing my internal IP address.
Network shares etc. would likely be somewhere on the same range and they could launch subsequent attacks to try to sniff confidential documents and resources.
The castle and moat model is obsolete anyway. Most attacks today come through "pulled" vectors that bypass the firewall. If you rely on a physical network perimeter for security your security is an illusion.
Prior to WebRTC you'd have to scan much larger IP ranges to try and find internal network webapps that are CORS enabled.
My ip address is 192.168.99.105
Script tries XSS attacks on:
http://192.168.99.1/ciscowebinterface/known_dodgy_admin?user=root&pass=NEVERCHANGED1
http://192.168.99.1/juniper/also_leaky_admin?user=root&pass=NEVERCHANGED2
http://192.168.99.2/... enumerated