What would be the benefits of rear spoilers in cars, like this one:
A spoiler is an automotive aerodynamic device whose intended design function is to 'spoil' unfavorable air movement across a body of a vehicle in motion, usually described as turbulence or drag.
A rear spoiler is designed to change the flow of air over the rear of the vehicle. This change in air flow increases downforce on the rear of the vehicle to help improve traction in an effort to prevent sliding while cornering.
What would be the benefits of rear spoilers in cars, like this one?
On cars like that one, there are no significant objective benefits. There are some disadvantages
On racing cars on racing tracks at high speeds, there can be increased downforce on the rear wheels which can aid grip in high-speed cornering and high-speed braking effectiveness.
A properly designed spoiler (unlike the one pictured) can reduce high-speed drag on cars that are otherwise not aerodynamically very efficient. This usually isn't a concern for typical use of cars like the one shown.
Cars marketed as "high performance" often don't have spoilers of the type shown (e.g. BMW M5)
The spoiler spoil the air flow at the rear side. When the car is cruising, from the frame of reference of the car, air flows around it from front to back. If the air flow is smooth and if there is a large velocity at the rear side then there will be pressure drop. Thus, there is a low pressure at the rear side and higher pressure on the front side, creating a drag.