"First, as I recall, it took Microsoft a long damn time to open up an appreciable lead on Nintendo - well after the Blessed Advent of Halo."
Actually it took a little over a year. The Xbox pulled ahead after Christmas 2002 and the Cube never caught up.
"Second, it is preposterous to suppose that the GC would have sold the same without those games; it would have become a genuine flop, not just a disappointment."
Well yes I suppose if 90% of the Gamecube's best games were not released the Cube would have done a lot worse.

"And lastly, you're reasoning as if Halo is the only difference between the Xbox and the GC. Which is especially odd coming from Ian, since he routinely hauls out a laundry list of mistakes he believes doomed the Cube extending far beyond individual titles."
Well I do believe that the Cube flopped largely because Nintendo seemed to f*ck up pretty much everything. Though I include an overreliance on franchises as part of it. One problem Nintendo has is that they are often accused of rehashing because they release too many franchise games. So Nintendo's response to that was to CONFIRM it by going hog wild on sequels.
I don't think that just the games is the reason the Cube didn't sell BUT I think if they were true system sellers people still would have bought a Cube. There were a lot of problems but the console still worked and was reliable and affordable. People put up with Playstations 1 & 2 even though it was practically a given your console would die within a few years because it had the games they wanted.
Plus franchises in general only sell for so long before they get stale in the eyes of the public. The system sellers of one generation usually don't have the same selling power next gen. Why buy a Cube for Mario? I don't need a Cube for that. But Halo. I NEEDED an Xbox for that. I NEEDED a PS2 for GTA in 3D. There was nothing comparable. System sellers provide an experience that you need the console for (or in the case of Halo's LAN stuff what ignorant people THINK they need the console for). Halo 3 actually won't sell as well as Halo 1 & 2 did BUT it's newer, cooler, and more popular than Metroid Prime (as unfair as that is) so it'll still kick its ass in sales.