is there anything about house points that would win Hermione or Harry more status than they would if they just kept getting good grades in class, answering questions correctly, and saving victims from bullies?

Sure. By earning house points, Harry and Hermione are essentially doing a favor for their houses independently of whatever they did to earn those points. It's a favor that's absolutely useless in functional terms (at least, I don't remember the House Cup granting any substantial perks), but that doesn't matter too much to the psychology involved; you're well above the 20 karma threshold but you still get a little spike of satisfaction when someone upvotes you, don't you? Same mechanism at play.

This is complicated slightly by the fact that House standing is zero-sum, but I still think in-house status gain would outweigh out-of-house status loss thanks to a number of considerations. Point allocations tend not to be announced to the entire school, for one thing.