In the case of WiFi, you use a password and WPA2?
Sure, if someone knows your WiFi password they could set up an "evil" router close to your house with the same SSID and credentials, or they could break into your house and install LAN wiretaps, but c'mon, if you are this paranoid you probably don't even have a smartphone in the first place.
Do you mean that you don’t need a way to verify the routers identity on the local network because it is already protected by a password?
Firstly, I don’t think that’s true because you add a lot of sketchy and unknown devices to your network over time (guests, streaming stick, computer with preinstalled OS…) so I wouldn’t trust every device in my WiFi.
And also, if you do trust your network, you don’t really need https inside it, right?