[citation needed] - I would say most people will primarily use LAN services in private home/corporate networks. But I don't have a citation either.
It's different use cases. Maybe one needs the warning, the other one not. But putting the warning on everything and overload the user with them is not the right solution.
Using a self signed CA is a pity, because installing it on every phone, tablet, laptop, tv, pc, ... is cumbersome in a home network, and making all hosts public and depending on an external CA for local resources to not get scary warnings can not be the right solution either.