iPhones have a setting named "Wifi Assist" where the phone automatically uses the cellular modem when the internet over Wifi doesn't work.

You should be able to connect to "broken" Wifi networks because you might actually want to access devices on the wifi network. For example, I want to be able to print things (my printer is on my home network) even if the cable modem is down. So my phone should just use cellular modem for internet, but still connect to the "broken" wifi.