A LAN should be using site-local addresses, rather than just link-local addreses.

Oops, not quite right there, but I suspect you misspoke. Site local addresses have been deprecated. I suspect you meant to say Unique Local Addresses (ULA), which were defined to deal with some issues that site-local doesn't work with.

But just to agree with your statement, you should definitely not be using link-local addresses for anything but routing configuration. I typically just think of it as a behind-the-scenes address (Router and neighbour solicitation/advertisement messages use it).