They kind of are the only options. All of these issues are sitting on a slippery slope. If you accept a technical solution that works well, then eventually somebody is going to push that further.

If you need to use your ID to log into a website (even if the website doesn't get any of your information) then society is only a step away from the government monitoring everything you do online. And at that point it's up to them to decide whether they want to do it or not, because you're already used to the process. If they decide to violate your privacy there's nothing you can do about it other than vaguely point at privacy laws before promptly getting ignored.