The biggest hassle would be that the embedded HTTPS server needs a trusted certificate, but certificates are only issued for hostnames, not IP addresses. So the embedded HTTPS server's certificate and LAN clients would need to know the hostname of the device running the app.
Cloudflare manages to provide a certificate for https://1.1.1.1. (But not reserved ones; see [1].)
Aside from that, what is the purpose of this comment supposed to be? (The general tone reads as if its meant to refute the parent; did you intend it to be a reply to chrisseaton instead—and thus a defense of the HTTPS-complicates-things position?)
That's correct, some CAs issue certificates for public IPs. You're never ever going to get a cert for a private IP, since these are not globally unique.
This isn't saying anything not already covered in the material I referenced in my comment—although it does say it less precisely, so I'd argue on those grounds that all things considered this comment need not have been posted...
(In any case, I'm totally mystified about why my own comment that includes that link and corrects the untrue statement about it not being possible possible to get certificates for IPs was deemed to offend someone's sensibilities. Surely the offense, if there is one, is in the comment that makes an outright, verifiably untrue claim?)
