You can buy a cheap domain to make sure no one else uses it and just roll it on your lan. Throw some DNS ACME challenges and you have valid certificates too.

I do it for the LE certificate. But "cheap" is subjective. Domain registration and management should not be as expensive as it is. Nothing the registrar or registry does could be worth $8/10/200 a year with guaranteed 5-10% price increases every year. It is a grift.

Why should I have to purchase something (yearly subscription, mind) in order to access something that is potentially half a meter away?

This is not how anything should work.