I'd love to see some data that can tell if speeding to the hospital (by random people, not by a trained ambulance driver) has a net positive effect on the outcome of the patients, as well as what the risk of car accidents happening as a result of the speeding.

I also wonder if maybe by forcing cars to go slower we could: 1) reduce car accidents by a lot and 2) reduce current spend on emergency response by a big enough amount that could then allow to use it to cover faster response times (e.g. sending a helicopter)

Indeed, it wouldn’t be speeding that would get you to a hospital many minutes faster; it would be judicious disregard for red lights and centre markings—much like ambulance drivers normally do by virtue of their sirens and lights.

Speeding doesn’t save nearly as much clock time as it feels like it does, especially if you’re regularly blocked in by other cars and traffic signals.

Speeding might get you through the lights before they turn red, though. A bad luck red sequence might altogether be avoided with some speeding. You might include "old green" in this as well, different regions have a different time from you getting red to others getting green.

Red lights themselves could often be somewhat safely ran through with some attention and a fast-accelerating vehicle—slow down first, check directions, etc. Preferably in particularly paying attention to pedestrians..