You would then have to add mechanical devices, which would likely be heavier (requiring even more support structure strength), that would have to move hundreds

You would then have to add mechanical devices, which would likely be heavier (requiring even more support structure strength), that would have to move hundreds or thousands of tons of building mass, and with high precision, and then return it to the initial position, while canceling the inertial forces to prevent it from ping-ponging and making it worse. I only have basic engineering knowledge but I can almost hear one of my professors screaming, 34 years later. :) Many tall buildings have a tuned mass damper near the top that helps to dampen oscillations. It doesn't require any active mechanical devices. Taipei 101 has it out in the open, you can easily find videos of it during earthquakes.