You have already answered why no one in their right mind would embed a shared certificate across all devices. I don't think you are being realistic with yourself when you believe people use self-signed certificates; they don't.
You are missing what happens instead. There is just simply no web management interface on the device anymore. You need to download the vendors app to configure and use the device. Maybe, if the vendor cares, they use their own CA to secure a local connection to the device. Much more likely, the app and device exclusively talk to their cloud and use that as a middleman to exchange information.
