That's more or less what Perspectives (https://perspectives-project.org/ https://perspectives-project.org/) set out to do: a bunch of notaries would crawl websi

That's more or less what Perspectives (https://perspectives-project.org/ https://perspectives-project.org/) set out to do: a bunch of notaries would crawl websites, note their TLS cert and distribute them to whoever would want to visit the site, to have a point of comparison. It didn't take off, mostly because of potential privacy problems and because there were not enough volunteers to make it scale properly. But the idea was sound.