So even if you had to drive 100 miles to the hospital, going at 100mph (the proposed limit) you are going to take an hour. Going at say 120mph you are going to get there just 10 minutes faster (50 minutes).

And this all assumes that there are no corners, no traffic lights, no other traffic etc - that you can just point your car directly at the hospital and hit 120mph and sit there for 50 minutes straight with no interruptions.

If you plan to average 120mph for 50 minutes of driving (to allow for corners, traffic, etc) then you are approaching Formula 1 car levels of speed (they average 138mph across a race), but in a non-F1 car, on a non-F1 surface/track, and a non-F1 skilled driver.

If you need to go less than 100 miles, say 10 or 20 miles then the time saving of going over 100 shrinks by orders of magnitude so the benefits of going over 100 shrink too.

This does not sound like a reasonable argument to me.

You still shouldn't be driving that fast. In your panic you're even more likely to make a mistake and end up killing yourself, your passenger and, potentially, another car full of people.

Emergency vehicles are involved in proportionally more accidents and they have trained drivers.