Part of the reason Formula 1 cars break up into pieces because the components that break are designed to be just strong enough to deal with the normal stresses on the car, not to deal with the stresses from impacts, in order to save weight. Even minor contact, such as another cars tire contacting a front wing component will often shear off the front wing component, and sometimes the contacting tire gets cut and goes flat.
The main component in driver safety in the cars is a combination of a very solid and padded cage (sort of like a helmet for the driver's body) that surrounds the drivers body, legs, and sides of the helmet, surrounded by components that collapse instead of shearing off. A few years ago, the rules were changed to not allow the drivers feet to extend beyond the front axle, effectively increasing the size of the crumple zone. The parts that crumple - collapse reduced the peak g force involved in a collision by having a lower rate of acceleration (deceleration) over a longer period of time. The impulse - change in momentum is the same, but the time is longer so the peak forces are smaller.
For some components that do shear off, like an entire wheel assembly, there is a safety factor in that the wheel assembly can shear off without bringing the entire car to a complete stop. The tradeoff here is that the sheared off components could hit other drivers (or rarely spectators).