I have definitely warmed up to the Quai de l'Ile since it was first introduced. I believe it was introduced at around the same time as the American 1921, and I was clearly distracted by the 1921 at the expense of almost every other watch. ;-)
I have no expertise in the matter, so I cannot really comment on why the QDI does or does not do well for VC. The personalization aspect of the QDI never really appealed to me. It is no secret that, for the most part, I love VC's designs, both vintage and modern, so I really do not see the need to insert myself into the design process by choosing metal combinations and colors, etc. I would rather leave that up to the professionals -- and having met Vincent Kauffmann and his fabulous design team, I am very comfortable with their designing any watches I might wear.
Like Alex, I much prefer the open dials over the solid dials in the QDI range. I felt that with the introduction of the solid dials, the line lost a bit of its edge and perhaps a defining design element. In the original generation, there were so many details to love about the QDI. The case architecture is gorgeous. I could stare at the case of a QDI all day. The transparent dial provides so much to look at and admire AND you get a view onto the top level of the movement, which is rare for a VC and worth the price of admission. I love the movement family deployed in the QDI and especially the treatment of the rotor. The QDI definitely possesses a lot of VC's DNA, but it is a watch that must be discovered. I am not sure it is easy to recognize it as a VC with only casual observation.
I do know that on the occasions when I have had a chance to try one on, I have felt that the QDI did not quite fit my wrist perfectly. But that is a very personal matter. I have definitely moved downward in watch sizes over the past several years. I am very comfortable with an Overseas on my wrist as well as a 36mm Historiques 1955, but I find the "new" Malte watches too big for my wrist. As I said, this is totally personal.
Price and relative value may be an issue. In the price range of the QDI one finds some really interesting and unique offerings from VC, models that are perhaps not as avant garde as the QDI and that might more clearly be identified as VC watches. I think of any one of the watches in the Historiques line, for instance. In fact, I have made those choices over the QDI in the past, and probably will again in the future. As you already pointed out, one could get a Patrimony or Traditionelle with a comparable or even the same movement at a better price and have a very beautiful timepiece on the wrist for less money. The Patrimony and Traditionelle watches are safer bets long-term when considering what will look good 10, 20 or 30 years from now.
All that said, the QDI, particularly the first generation with open dials, is a gorgeous and bold watch that I would not mind having in my collection. I wonder if the QDI will be better appreciated by collectors some years from now especially if the line is discontinued.
Best,
respo