There is a main story for this game that ends in 2 years, turn this school around.
The main story is to turn the school from bad to good for grades.
This is told to you in the beginning of the game.
"Turn the school around" is a goal, not a story. In fact, what I see is a premise or a setting, NOT a story. At best, the story in HHS would be
the things you do during those two years, but again - there is no "ending", because, regardless of how well you do, the game does
not end. Which brings us to the 2-year limit, which is the only "ending"...and has nothing to do with the world setting; it exists, as you said, because the game starts breaking down afterwards - a technical aspect.
Anyway, not buying it. HHS is a [simplified] sandbox game, those lack a story by design. How the player approaches the challenges provided by the
setting is what makes a
story, unique to that one playthrough (RIP my Drugville)
.
If I had to have a point, it would be this: what IS "the beginning" for a game that has no order of things, in the first place? That was the reason I asked for clarification on the "full walkthrough from beginning" part.