That's an oversimplification. WH could also reach out and offer to work out a deal with the site owner to license use of their trademark. That would probably entail some compensation (which could be anything from "good will" or a token cash amount, up to millions of dollars) and probably some verbiage on the page reading something along the lines of "Logos and identifiers on this page are the property of Waffle House, Inc and are used under license" or whatever.
of course i would love to live in a world where waffle house can be as off the rails whimsy as kfc, but im just pointing out why not to get your hopes too high!
After the initial legal letter they could have licensed / agreed to the usage, or taken over the running of the website. There are several ways to protect their trademark without being killjoys.
The equivalent would be a simple text list of all Waffle Houses currently closed, sourced by physically visiting each location and noting any closures. The author here used Waffle House's branding and logos, and also sourced the data by scraping their web site.
The Economist editors don’t blog to reproduce every letter they receive from attorneys, and they don’t taunt McDonald’s on social media, and probably don’t host the website that tracks operational status of soft serve machines.