If RE2 were to be remade, I'd also prefer an over the shoulder view. But everything else should be almost unchanged.
- Keep the inventory the same, so you actually have to do some item management.
- No uber melee, being able to roundhouse kick heads off or counters. Though I wouldn't mind to see RE6's dodge system in a Remake. But in turn make enemies like Lickers one hit kill enemies.
- Limited ammo. Sure, you could now easily head shoot Zombies with OTS aiming, but you should have so little ammo, that the better solution is to avoid them altogether.
- No checkpoints and only being able to save at Typewriters. Keeps up the pressure to be careful, because you can only save at one place.
Now for the biggest change, that I'd really like to see.
- Optional Co-op. You can play alone in single player, or co-op with a friend. No co-op AI. You have the option to play the story like back in the day, with either Leon or Claire, or together with a friend. Should you play co-op, scenarios, events and maybe even boss battles could change. Maybe even have area you couldn't reach before, because you didn't have a friend that could give you a leg-up.