Here is the answer without using any math.....
You need the long springs to bias the weight of the top toward what I'll call "neutral bouyancy".
Think about it this way....we have gravity acting downward all day long.....So picture getting in the van and lifting the top with no springs installed. It will take a superhero to get it up, and it will come crashing down when you let go.
If the spring load is too high, then the top would stay popped up and you could hang from the roof and it wouldn't come down.
When the spring rate and preload are correct, the top will stay in any position that you place it, from all the way down to all the way up.....this is what we want, same for a garage door BTW.
When this condition is achieved, we are essentially just overcoming frictional losses of the pivots, sliding elements etc when lifting and lowering the top....at least on paper. The reality is that the geometry of the crossbars and where the springs attach make things somewhat non-linear, that's why we need trig and free-body diagrams.
So with the weight of the top balanced with the springs, the forces required to lift and lower are small compared to not having the springs to balance the weight..essentially the forces need to be high enough to overcome friction and deal with the non-linearities of the geometry.
When the actuator force requirements are low, the actuators can be smaller, cost less and use less power, just like people who are lifting the top (except for the cost part
The other benefit of the springs is that if an actuator fails, the weight of the top is balanced and won't come crashing down and injure and maim you or your loved ones.