Nothing prevents serving this style of login from a front page that offers everything you just mentioned as an alternative. Groaning may express dismay but -- this is mere inconvenience we're dealing with here.
There's no button to create a new account or find a forgotten password. There's no reasonable way to logout. It's usable for a site with a trainable user base, like a small club or employees, but I wouldn't expect anything intended for public use to do it. I've experienced one public site that used it for its members only (subscription) content, but I think they've switched to forms and cookies.
> the nice thing about this is that the browser will keep sending the credentials to subsequent requests of the same domain until it receives a 401 status as response.
The logout button can simply redirect to a static page that returns a 401.
You would have to rewrite HTML5 and handle all HTTP traffic manually to set the Authentication header for every request. OP's trick of HTTP + ancient browser spec for handling basic auth triggers automatic sending of the Auth header for all requests.
> the nice thing about this is that the browser will keep sending the credentials to subsequent requests of the same domain until it receives a 401 status as response.
You don't need to set anything, just send a 401 if you want the browser to stop sending credentials. You don't even need cookies.