I take apart the router, and get a valid certificate
You only get a valid certificate for your router's address. But if you can take apart the router, you don't need to hijack the DNS, you can simply control its traffic.
But if you're a guest in my home and I see you take apart my router, you'll have to answer a few questions. Same in an office or coffeshop. Having LAN access doesn't mean you have complete physical control of the router. So the HTTPS is not useless.
Considering basically every router has the same address
They have the same IP address, not necessarily the same DNS hostname, which is what the certificates are tied to. The user would just be told to connect to the hostname (possibly printed in the sticker) rather than to the IP.
That's certainly one option, but what happens now if I change the IP of the router in its config, because I use multiple in my LAN, one as router, the others as AP?
There is no option for any of this that isn't completely messy and hacky
I take apart the router, and get a valid certificate. Now I hijack DNS, and get you to connect to me.
HTTPS within LAN for this purpose is useless.