On higher skill levels the zombies move more quickly, meaning that you'll need to take them down faster to avoid being hit. The SMG is fine for taking out individual zombies, but it just doesn't cut it for dealing with crowds. For that you'll need a weapon capable of piercing the front line of zombies and damaging lots of them at once. The Shocker and Ripper are by far the best for this and I'd say that either one of them (fully upgraded) is a must-have tool for getting through Chapter 10 on Grim and above.
The SMG is also (IIRC) the most expensive weapon to fully upgrade, meaning that you'll be sacrificing upgrades on weapons that would be more helpful to you during the toughest parts of the game.