> Failure leads to weird redirects for which you can't really fall back to a login prompt because the auth happens on TLS level and a token in HTTP can't replace that.

That's not true. nginx, for example, let's you return a custom response, which can easily be a 302 to the login page.

But I agree with all other points. On a sidenote, there's also the great option of using a CA for your client certificates while still using a normal CA for your https certificate - you don't have the worry of installing a root certificate on all clients and still have a nice, valid https connection in the browser. Unfortunately, hardly any tutorials pointed this out and used their own CA for everything instead.