All new showerheads are limited to 2.5gpm. If you have an old one, it could be quite a bit more. That being said, it still shouldn't back up. A vent doesn't affect the draining much, it is to prevent siphoning adjacent drains dry because the displaced air has no place to go.
The slope of the drain line may not be correct, or they may not have done a good job snaking the line.