Why is the DVD/Blu-ray called The Complete First Season?...

It's probably labelled as "the complete first season" because the packaging had already been designed and approved before production on Season 2 was halted.

"Why did HBO even shoot any of season 2, when they knew they wanted to cancel the show after the first two or three episodes aired?"

So let me get this straight: you think that HBO ordered another season of a show they had wanted to cancel since its first few episodes aired, then went into production on the new season (which means ordering scripts, contracting actors, writers and directors, securing locations, etc.), all the while trying to come up with some pretext for axing the show when they'd already spent all the time and money necessary to have produced 2 1/2 new episodes?!?

If they wanted to cancel it, they would have done so after Season 1 aired, end of story. They pulled the plug on "Deadwood" after three seasons, leaving no opportunity for that story's resolution; the same happened with Milch's subsequent HBO show "John From Cincinnati" after just one season. No doubt the actors' contracts for "Luck" were paid off, but that's because they were all signed for a full season's worth of work that they weren't able to do.

And the story about horse deaths wasn't "fake." The whole reason that production was suspended and the show ultimately cancelled was because HBO didn't want to take the heat for any more animal deaths--so why would they make up a story about animal deaths and garner themselves a lot of unnecessarily bad publicity when they could have just said that the show was too expensive or that enough people weren't watching it?



"You can keep the gum."

Why couldn't they just release the finished Season 2 episode on the set and call it The Complete Series?