The safety angle comes about because the suspension determines how a car behaves in terms of its handling and also its road-holding, or grip. Any suspension system is designed to make the most of the tyres.
A given tyre will produce more grip the more force there is pushing it onto the road. This part of the suspension's job is to apply that force as the car starts to turn into a bend.
The suspension also needs to absorb imperfections in the road. Without it, every bump and pothole would be transferred directly to the car and your passengers.