Even in your made up thought experiment that accounts for << 1% of all aggressive driving miles I still think this is the correct approach to take. Speeding to the hospital is only superficially different than speeding and weaving through traffic on your morning commute. The biggest difference is probably that you are flustered, and less likely to make good decisions while in route. The worst accident I have ever seen was someone rushing to the hospital [1]. The threat to those around you, and the chances of an accident slowing you down outweigh the small potential time saved. It would be far better for you to learn first aid and respond appropriately than for you to drive aggressively to the hospital.
[1] So there I was[2] driving through Iraq when an Iraqi army convoy approached rapidly from behind us. While swerving past my trucks, that had pulled over for them to pass, one of the vehicles left the road and rolled over multiple times. 2 people died in that accident, I applied tourniquets to 2 additional people who lost limbs, and no, they didn't get the gunshot victim to the hospital any quicker that way.
[2] Fun fact. Do you know the difference between a fairy-tale and a war story? War stories start with "So there I was".
Emergency vehicles rushing around may or may not be good overall. They have a few advantages over your average crazy driver though such as lights and sirens to get the other vehicles attention so they can move out of the way.
Police often have additional driver's training. I happen to think that police often drive faster than they should, but this is less the case for emergency vehicles. I rarely see an ambulance or fire truck moving at high speed. They are pretty aware of their job to get somewhere safely, and I am typically only passed by an ambulance if I am stuck in traffic myself.
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