If someone intentionally muted the phone to prevent calling it, they probably would have walked or ran away from you with the phone. Or they would have shut the phone down to prevent any tracking. Yes it's not as fast but you can login to the find app or website on another phone or device.
Yes normally trying to shut down a locked phone doesn't work, but there's an emergency shutdown that always works on every phone.
Sound isn't really a security thing.
Network settings are locked for security, that's ensure the find features keep working