Those dialogs were a bad idea in browsers (and have been gradually going away) too. Never do this in new software.
Treat "Cert is broken" the exact same way you'd handle not being able to connect. Don't treat it as something you can just cross your fingers and ignore.
As a user i really dislike this because more often than not certs are broken because the server is temporarily badly configured (instead of some malicious reason) and i do not even care about it (or even if it was compromised really) as all i care about is read some page's content, connect to some messaging server (Pidgin often had issues with -IIRC- MSN servers), etc.
Of course if it is about, e.g., downloading some application (like an auto-upgrade mechanism) then sure treat it like that. But in other cases let the user decide, even if such sort of decision is made opt-in.
The device doesn't _need_ a certificate for a "local" (presumably RFC1918) 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 a typical consumer network every device is getting a (more/less) random ip address by dhcp. So there is no guarantee that the dns name will always point to the right ip address, therefore it is impossible to use a fixed dns name. This fact makes it impossible to get a valid certificate. Especially not from 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...
Treat "Cert is broken" the exact same way you'd handle not being able to connect. Don't treat it as something you can just cross your fingers and ignore.