What about local management software listening on some ip address? (e.g. routers?)
There will never be a valid certificate for a local ip address.
It needs a certificate for its name, and arranging to have a valid (by which I'm assuming you mean trusted in browsers) certificate for a name isn't hard. Sectigo and DigiCert both offer vendors a suitable product for that purpose last I checked. If you're making a short run hobby product you could just use Let's Encrypt.
In easy words: You use example.com for your IoT device. Where should example.com point to? To all possible ip addresses? I don’t think so...
Besides that you need a private key on the iot device for decrypting the tls traffic, imagine somebody gets access to the device and now can basically mitm all other devices...