Well, until they make Hogwarts: Th' Game for PS3/360/Wii, we'll just have to be content with the older games... /sadface
Did anyone ever play the Game Boy Color games? Lord I fell in deep and platonic love with those. I'm with y'all on open-world utterly pwning story-driven - the best part of the first two games (and to an extent the third) was the freedom to do whatever you wanted: that experience of being a student at Hogwarts. Which is why they need to get a shuftie on with H:TG! Warning: incoming daydream alert...
It wouldn't be a MMORPG - nope, the other students would all be CPUs, with lots and lotsa different dialogues all penned by Rowling herself. Like KOTOR! But more. You'd customise your character model to within inches of your true actual self and roam the castle, engaging in midnight escapades whenever you wanted. Also Peeves! There'd be new characters - a new Defence Professor, for sure, this all taking place after the War. And new enemies - not Voldemort, more Malfoy-esque, perhaps based in more hidden Slytherin-y chambers within the castle itself.
After a week you'd know nearly all the secret passages, and use them more frequently than the stairs. There'd be sidequests ad infinitum - some issued by teachers, some not. All the Pottermore content would be there in some shape or form, naturally, and you'd be Sorted, getting to explore all the House-specific areas that Harry never saw. Maybe you'd pick up an adoring house-elf somewhere along the line; maybe you'd strike up a friendship with Hagrid. And Quidditch would finally, finally be fleshed out into a full PES-type sub-game.
There would be an overarching good vs. evil story - but you wouldn't have to complete it if you didn't want to. Most students aren't Harry, after all. Smaller victories, like escaping detentions or duelling Prefects might suffice. There'd be a few cameos from existing Potter celebrities, and Hermione would be back for her seventh year as you started your second or third, but mostly you'd splash happily about in the deluge of new characters. Including the twenty-or-so NPCs available for you to pick and choose your best friends from.
Oh, and you wouldn't have to be good. Slytherin or no, the option would be open to play as an utter scumbag from start to finish. Backstabbing, manipulating, political swerving: the floor would be yours. It'd be as close to actually attending Hogwarts as you could ever reasonably get.
...But we won't see it, I shouldn't think. Not in this lifetime. If only cos the effort required to make the game everything it should be would take twice as long.
*slopes off to cry in a corner*
EDIT: Also, proper voice acting. You'd sidestep the problem of spending all the budget on millionaire movie stars just by having an all-new cast of characters (though Emma Watson or bust), but it goes without saying, really, that this version of Hogwarts would be as immersive as it gets.