Many vegetables actually have solid protein on a protein/calorie basis. Comparable to milk. Low net carbs is not really possible with low protein, short of chugging crisco.
Vegetables contain a lot of fiber, the soluble kind in particular tends to lock up sugars in a goop that passes through the small intestine and makes you fart.
You can graze constantly on plain intact produce and you won't get fat.
If Im exercising 5-6x a week and I can't eat much protein I need calories from somewhere.