If the router is also the modem, it can have diagnostic stuff that could (I am careful to point out: theoretically) cause them a big support headache in one way or another.

Also, I had a DSL modem back in the day with its own terrible NAT built-in. I managed to log in (I may have been given the admin password from a friend who worked at the ISP, allegedly) and once I put it into bridge mode, I was able to acquire multiple public IPv4 addresses via DHCP.