Sure. I'll try
If the chassis has a much higher spring rate than the springs (and tires) then increasing its rigidity is going to have a minimal effect on the overall response to any input. I think this will make more sense when we get to your last question below. Input could be a distance traveled, like a 2" deep step in the road surface. But it also could be weight transfer in a corner, or braking or accelerating. It's just more equations to figure out. hahahaha

Why stiffen the chassis then?
Well most folks here are increasing the tire traction, and often spring rates. Some chassis (eg convertables) already start with less rigidity and others were intended for uses where it could be an issue. So the factory dealt with the potential issue. Transfering the weight to the rear the way drag racers did even in the 60s was more than a production chassis was deisgned for. My co-worker used to put his GTX on jackstands after a night at the dragstrip so it would settle back to normal.

The other reason is that its a variable you just want to make sure is eliminatated from the picture if at all possible. It's a big undamped spring and another variable. Is it essential? Well no. There have been successful vehicles with lots of chassis movement, Morgans come most immediately to my mind. Basically in the real world its a pretty good bang for the buck IF for almost any use involving slicks or r-comps. The downsides are weight, cost, obstructing other uses/access to interior and time to design and test. In the end its about what the rules allow and what makes sense for you.


Is it analogous to increasing the spring rate? Well yes and no. Yes the equivalent spring rate has increased, assuming it acts like a linear spring. No, that's not the equations for dynamic response. Basically a differential equation is solved for using Mass that is sprung, the mass(s) that are unsprung, the spring rates and damping rates that are connecting the sprung to unsprung masses. Dynamic analysis is about system response to input (distance, force) over time.
Notice how mass shows up again? Everyone wants to put on big this and bigger that or for you to buy their gizmogadjet, but the real game is reducing mass.