I haven't ever seen or run one of those rocks --but simple math shows they are not masonry heaters...
The heat capacity of the stone might store 15-20 minutes of output (while a heavy steel stove could probably store 10 minutes). So, there might be a 5-10 minute extra lag on startup, and 5-10 minutes of extra heat a couple hours later, doesn't sound like a big (or even noticeable w/o confirmation bias) difference. As for 'spikes', I have never seen my stove 'spike' over a time scale shorter than 40 minutes, I don't think the extra 10 minutes of storage is going to spread or 'soften' that out much. I expect much of the positive testimonials are more related to differences in convection/radiation heat xfer and radiant surface area than 'storage'.
If some folks think they're pretty, and have the $$, they should go for it. But in a 'blind taste test', I suspect most people couldn't tell the difference in heating standing 3 feet away.
Edit: we discussed heat capacity here:
https://www.hearth.com/talk/threads/42152/