The future of gaming lays in the hands of those who can tap into the mediums greatest power interactive fiction. The more we care about what is going on (the narrative) the more engaged we are. Look at what sells. The Last of Us. GTAV. Mass Effect 1/2/3. Uncharted. MGS 1/2/3/4/PeaceWalker/ and now 5. Tall Tale's The Walking Dead. Batman Arkham Franchise (which has Dennie O'neal himself writing it!) The best selling games that pull us into the gameplay have great stories. Not just great, but multi-faceted with many potential outcomes. Why would we smack Sonic in the face by railroading and watering down his persona with a scant plot? If you want a mindless platformer go buy Angry Birds. It's cheaper.
As a game designer, I couldn't disagree with you more. You did hit upon the key word,
interactive. Interactivity is the thing that separates video games from other media. Therefore, any good use of the medium will stress its interactivity. But interactivity is in fact so central to the experience that I would say that any story should be in service of the interactivity, not the other way around. In fact, story often interferes with interactivity. The more time you're watching cutscenes or canned conversations, the less time you're spending interacting. That's why a lot of people (myself included) don't care too much for the Metal Gear series. I was totally into MGS1 when I was a teen, but now it's just blah blah nuclear warheads blah blah FOXDIE blah. Shut up and let me play!! And yet those of us playing for the first time don't want to skip those scenes because we're afraid we'll miss something.
Sometimes a story can be woven into a game to give a good interactive experience, but IMO this is when the story is a fundamental part of the game and not something that's just tacked on. Let's consider a game like Doom. What do you do in Doom? You shoot monsters, grab powerups, get keys, unlock doors. The story might give you a reason why you're doing those things, but why you're doing them isn't important. Doom I and II restricted the story to the manual and a screen of text at the end of each episode. And you know what? I love it! Doom is a blast. I'm not here to find out what happened to the laboratory. I'm here to blow shit up!
Now consider a game like The Last Express, where you're trying to solve a murder. What do you do in The Last Express? You go from place to place, collecting evidence and listening for clues. You can't very well solve a murder without knowing who's involved, why, and how, so in this case, the story has everything to do with the gameplay.
Then there's the text adventure A Mind Forever Voyaging, which is a very interesting case. In this game you're a computer running a simulation of a city a few decades in the future to simulate a new economic plan. You spend most of your time walking around this simulated city as a simulated resident named Perry, recording everything of interest. In this case, the story
is the game. It's "on rails" a bit in the sense that the overall plot progression is the same no matter what the player does, but it's still a highly interactive game; you get to choose what Perry sees and does, and it affects your experience. It feels like you're really in this big complex simulation of a town, its secrets waiting to be uncovered. You feel directly involved.
And this is a stark contrast to, say, an RPG. What do you do in an RPG? Walk from place to place (whee), fight monsters, maybe solve the occasional puzzle. The story will dictate where you go next, and very occasionally it will tie into a puzzle, but that's it. It's bolted on; it's not involved with the gameplay much at all. And with a lot of classic JRPGs, if you take away all the dialogue and the story, you'll realize it's not much of a game. You're just hitting the "attack" button over and over. Welcome to why I don't play many RPGs anymore.
In summary, it depends entirely on the game. If you want a story, make the gameplay about the story. Otherwise, just leave it all out, or make your story as a novel or screenplay instead of a game. I don't know why so many designers insist on giving their games a story that has nothing to do with the gameplay. What's the point?