Bad HP OCs happen when they end up doing:

- Pureblood in any House, totally misunderstood and an outcast, but a powerful witch/wizard.

- Mudblood who is bullied by purebloods, friendless but clever and loved by teachers alike, has a special pet.

- A son/daughter of a canon character who has zero flaws and yet is burdened by their expectations.

- An OC who is an animagus but keeps it to themselves, somehow also has a timer tuner so they skip classes to frolic on the grounds, only to go back in time and still get all As.

- A muggle struggling with being a witch/wizard, is also homesick and cries a lot. Then finds they have a knack for flying and gets on the team in their first year, still ends up being mopey.

I've seen plenty of cliche things, whether they're paired up with a canon or not.