Well, this is an interesting amateur experiment (8-min video):
https://youtu.be/saWIxN05QFU
Although I don't entirely agree with his conclusions as to why we
don't see them in use by NASA. My off-the-cuff thought is that you
either want to avoid spinning the payload on the way down, or the issues
involved when /multiple/ chutes are required -- spinning parachutes,
used in pairs/triples/more seem awfully likely to tangle each other up.
The other "obvious" reason would seem to be that, just looking at
it, a VRD is probably harder to pack and deploy reliably, which probably
explains why we don't see them in amateur rocket use (that I've ever
seen, anyway). When you need reliability above all else (and simplicity
a close second), I imagine a VRD wouldn't offer enough benefits to
outweigh the risks.
That said, it sure /looks/ cool. And seems to have better
oscillation stability. Would it have better wind immunity as a side effect?