At one of the datacenters I used to work in regularly the SAN engineers were always up for demonstrating the base isolation of their Hitachi storage array - The whole thing sat on a plate atop a ball-bearing pit, and could be shoved about a foot in any direction. Which they would invite you to do. Given the weight of the unit you'd never get it to budge more than a cm but they had videos of it during earthquakes showing it moving around the full range of motion.
It was very 'v1' as far as base isolation goes and their newer equipment has more sophisticated protection, but it's an interesting field. On a larger scale the use of damping weight to protect entire buildings is amazing to see: https://youtu.be/NYSgd1XSZXc
The article demonstrates a multi-axis base for dampening the force imparted by S-waves, generated by Earthquakes, to artwork. But earthquakes also generate longitudinal waves (P-waves). I wonder whether P-waves are strong enough to damage artwork and whether a system should also be put in place to protect against them.
I thought the design of the isolator with it's angled ramps was clever (watch the video at the bottom of the article). But as you say, there's no protection in the vertical direction. My time in California has been limited, so I don't know what the z-axis velocities and displacements would be like in a significant earthquake. Since they spent a non-trivial amount of money on designing this, I can only assume the consultants & engineers took that into account.
It's quite intriguing, and I suppose I've just never thought of it that way, that you can base isolate individual objects.