It broke it in the sense that it removed a signal that would allow the service to distinguish legit users from possibly malicious ones. In the case of a legit user that has in the past always authenticated from an IP address or address block geolocated to say, Seattle, the service can look at any authentication attempt from elsewhere as anomalous and raise additional challenges.

However, with Relay, that signal is lost. Legit users and malicious parties become indistinguishable. The service can't tell if traffic from the relay is from a customer or an attacker.

What to do? Trust everything? Not good. Treat everything as potentially malicious? Safe, but makes the user experience worse.

To use your analogy, if you look through your peephole and can't tell if the person is your best friend or your worst enemy, how do you react? If you assume it's your best friend, you could be in trouble. If you treat the visitor like your worst enemy, you've pissed off your best friend.