Routers today are already dealing with this problem because Chrome throws major security warnings for any unencrypted HTTP traffic. The current solutions I've seen are to use things like Let's Encrypt/ACME certificates for wildcard sub-domains *.routercompanylocal.tld and a bit of secure handshake magic to register temporary A/AAAA records for link-local IP addresses (DNS has no problem advertising link-local addresses) and pass the private parts of the certificate down to the local hardware. Several major consumer routers I've seen will auto-route users to something like https://some-guid.theircompanyrouterlocal.tld and everything just works including a CA chain usually up to Let's Encrypt.

Doing Let's Encrypt/ACME for random localnet web pages is getting easier all the time and anyone can use that wildcard domain loophole if they want to build their own secure bootstrap protocols for localnet. It would be great if the ACME protocol more directly supported it than through the wildcard domain name loopholes currently in use, and that may come with time/demand. I imagine there are a lot of hard security questions that would need to be answered before a generally available "localnet ACME" could be devised (obviously every router manufacturer is currently keeping their secure handshakes proprietary because they can't afford to leak those certificates to would be MITM attacks), but I'm sure a lot of smart minds exist to build it given enough time and priority.