I'm not sure you are using terms here consistently. Nor am I sure what you are paraphrasing there.
Of course "stiffness" is important,
if that's an actual parameter to your model.
But if it's just the result of other parameters, then no, it's not important, it's just a derived value, or an emergent value.
Compare it with the center of gravity (or center of mass of a spaceship). Is that an important position, sure. It's the point about which the system will tend to rotate. But it's just an emergent position, the average of the mass of the full system.
The "center of stiffness" of the entire building is just a calculated point in space. Since you've been Googling this I'm sure you've seen this slide:
It's perhaps a useful point for doing calculations on individual members, or an an elastic system. But if
the system is deforming inelastically it's not really relevant.