> Is it a nanny-state that there are speed limits?

No, speed limits are fine. Its enforcing them with technological tools that are not under control of the citizen that is not fine.

Also, at least in my country, the code says that I am allowed to break the speed limit if there is a good enough reason (e.g. I am trying to escape from somebody that wants to kill me, I am bringing somebody urgently to the hospital because he may otherwise die).

For example one of my friends was born during the Oil Crisis of the 70s, and at the time car circulation was limited (odd plates one day, even plates the other). Both the parents had the "wrong" plate that day, but they decided to use the car anyway because it was an emergency. They got stopped by the police, and once understanding the issue, the police escorted them to the hospital with siren and lights.

How do you do that with externally imposed limit ? You don't (sorry your kid didn't make it, but that's the law) ? You prescribe a button that says "I'm in emergency" ? (no-one drunk enough will ever use it, I am sure, and neither will criminals using a stolen car).

Also in general there is the issue that in a healthy society most people will respect the law, and only a few break it. Putting restrictions on otherwise law-abiding citizens tells them the state doesn't trust them, and in the long term citizens will answer in kind.

edit: I will add that even if it were against the law, in some cases breaking the law and paying the consequences (paying fine, losing license) may still be worth it if it is an actual emergency.

You're still going to need traditional enforcement. The people doing those sorts of speeds modify their cars will just push a new tune to remove it (remember, most cars today are limited by the factory well before that to match tire speed ratings). So there's already evidence that limits set today do nothing to prevent this sort of abuse.