Should you change the router password for when you put in the router IP and are asked to enter a password or it doesn't matter security wise?

I know you should use a strong password for wifi but I don't use wifi and keep connected by wire and shut off wifi.

But there are two passwords for my router, the wifi one, and the admin password for the router.

Is it advised to change the router password or does it not matter in terms of hackers? ie would it only be accessible locally or via the internet as well.

If the former I would say it was not pertinent to change it since no one accesses my flat etc, that is not a security issue but if the latter I guess it should be changed.

So which is it? is it accessible from the internet or only locally? I am talking about when you put in the router IP address and are taken to the admin setting page for the router.