Personally, I treat high-budget AAA games as their own category, and appreciate them in their own way.
Consider e.g. Mass Effect trilogy. I absolutely LOVED those games, even though they were basically an interactive movie. They could've probably made ME as a visual novel, and the gist of the story would stay the same. Still, the form of the game was perfect, and was completely enjoyable as long as you didn't expect too much from it. It's not Minecraft in space.
The problem IMO is when game producers try to mix elements from other types of games into AAA movie-games. It fails, I think, because high-end AAA graphics are so hand-optimized that any attempt at giving players freedom of creation will start breaking stuff.
Mass Effect 1, at least, was most fun when you said to hell with the official objectives and just started treating it as a sandbox. I had so much fun using the sniper rifle from as far away as possible, or taking the mako places it really shouldn't have been able to go
Absolutely. But the flipside of this is that Minecraft has no story. It's sort of up to you as a player to do what you want and make your own adventure. Naughty Dog, on the other hand, is famous for their games' stories. I suspect interactivity and story are at odds. I also agree that the more sandbox-y a game is, the harder it is to make it compelling for a long amount of time.
I personally don't think one end of the spectrum is better or worse than the other. There are games with extremely limited interactivity (walking simulators) that I've had a blast "playing". I've also sunk a ton of hours into Minecraft.