How Important Are the Rear Shocks / Struts

It depends vehicle specs, road conditions and driving habits.

Shock absorbers are not carry the weight of the car, they are basically dampers. They restrict the amount of movement. In case of bump they compress and allow certain amount of resistance to slow down the movement. In rebound, basically the same function.

So, without them, related wheel tend to bounce in case of wheel hit a bump. Some of that movement could be transferred to the chassis dependent to the situation. Tire contact could be problematic on rough surfaces and this tend to lead difficult handling.

Without rear shocks; 1 - Understeer can occur due to soft rear end. Too soft rear could lead to weight transfer to the rear end (even though roll bar still attached) and could result decreased grip on front end (inside wheel especially during cornering). 2 - Abnormal tire wear could be expected in long term use. 3 - Depend to the road conditions it could be uncomfortable ride for passengers. 4 - RWD drivers could expect easy corner exit but difficult turn-in. FWD drivers also could experience more frequent power steering during exiting the corners.

In overall, depending to the car, road and driver, handling characteristics of the car will be changed due to the weight transfer issue.

Wait what? Let's look at some physics here.

If you have less grip in the front, your car understeers, you hit the tree and you die.

If you have less grip in the rear, you ovesteer, you hit the tree and die again, not seeing what killed you.

1. Rear end Grip Shocks are important to maintain the balance of the vehicle in a turn and ensure contact of the tire with the surface as much as possible. When shocks are no longer performing as expected, wheels would bounce, reducing the time of contact and thus available grip.

2. More rear end grip Once wheels are bouncing, the tires would ge tout of round pretty quickly causing even more bouncing, road noise, grip issues.

3. Chassis balance If you would hit a pothhole or a bump in a turn, your car chassis would bounce uncontrollably for some time causing all kinds of unusual forces on your chassis. You are risking spinning off into a ditch and potentially rolling your vehicle.