I have had an innicycle headset for I think 5 years now and its been on a couple different bikes.
The other reason I like it, besides what I mentioned earlier in this thread, is it looks less goofy than a long quill stem when I have it on frames that are a little too small. At least it looks less goofy to me. The two bikes I have used it on are 80s road bikes that are 2cm or so too short, so extra spacers get used. I think it looks less goofy compared to a Technomic stem because the spacers are basically the same size as the head tube and so it flows a bit better.
...or maybe I am just lying to myself.

Sadly, the bike that has the innicycle headset is on my trainer right now! Not much reason to have an expensive headset on a trainer bike, but whatever.