An example of a situation where a large coefficient of static friction comes into play is when you try to push a heavy object, such as a large boulder or a car, on a rough surface.
Consider the scenario of trying to push a car that is stuck on a muddy road. The wheels of the car have a large coefficient of static friction with the muddy surface. As you apply force to push the car, the static friction force resists the motion and prevents the wheels from slipping. The magnitude of the static friction force depends on the coefficient of static friction and the normal force exerted by the car on the muddy surface.
In this situation, a large coefficient of static friction is required to overcome the resistance provided by the muddy surface and initiate the motion of the car. If the coefficient of static friction is small, it would be more difficult to overcome the resistance, and the car would be more likely to remain stuck.
So, a large coefficient of static friction is necessary to provide sufficient grip or traction between surfaces to prevent slipping or sliding and allow for the initiation of motion in situations involving heavy objects on rough or challenging surfaces.