What if your DHCP doesn't give you a private IP address? When I was at the University of Michigan, my personal laptop always received a public IP address. Or if I'm in a pure-IPv6 setup, using prefix delegation/SLAAC? This problem is a lot harder than "just use the RFC1918 list of reserved private IP ranges".
The UMich network isn't "improperly configured". NAT-less networks have been around since the beginning of the Internet, and IPv6 networks don't use NAT (unless they're accessing IPv4-only targets, but that's CGNAT). I think you'll find a great deal of university/research settings have networks configured without NAT. If you can come up with a solution that works in all cases, I'd love to hear it.