Possibly the only reason for the vegetables in the dog food that you make at home is for the various pigments (carotenoids), some of the natural phytins, terpenoids, fiber, both soluble and roughage and finally and most importantly, feeding beneficial bacteria in the G.I. tract that depend on a small amount of plant material.
But in order for a home cooked diet based on low carb to work, you need to exclude potatoes and corn, peas and limas because they are naturally starchy.
I have been recommending Asian stirfry vegetables and even uploaded a picture of the vegetables I recommend.
Today, my wife came home with the other kind of vegetable pack usually available in large amounts in the frozen food section at the grocery store and it’s called “Normandy mix.” This is another very low starch mix vegetables that’s rich in soluble fiber and carotenoid pigments. See below