F1 cars are dangerous things. F1 tracks even moreso (when the race it still taking place). They are going to move very slowly and deliberately, checking and double checking all the safety features of the car. They are going to be very careful moving the driver, to avoid potentially exacerbating an injury.

If, on the other hand, they know the driver is dead in a couple minutes without intervention, some of those steps are going to get skipped (that's what I meant by the "acceptable level of risk" changing).

For what it's worth, I'm a firefighter/paramedic, and have cut many people out of (ordinary) cars over the past decade or so.