Yes, that would work.
It still sucks that if I want a browser on my LAN to talk with a server on the same LAN, I now somehow still need internet access (to renew the cert), need at least two accounts on 3rd part cloud services (the domain registrar and Let's Encrypt) and have to continuously pay for the domain.
Oh, and also have to mess around with the DNS configuration on the router, so the domain is correctly resolved to your LAN IP inside the network, but does not have A/AAAA records on the internet.
Also, this solves this problem for geeks with some knowledge of network protocols, but it still leaves everyone stranded who would like to run a local server but has no deep technical knowledge.
Finally, it's impossible to solve this problem in a large-scale manner, i.e. for devices you want to sell. Which is why the access menus for home routers will probably still stay on plaintext HTTP.