When there tends to be conflicting data on a subject, I personally use common sense and logic to determine my course of action. For the vast majority of human history, humans have lived and eaten veggies (Arctic cultures have limited exposure, I know, and they may just show that veggies aren't necessary but that's not the topic at hand). This isn't a recent phenomenon like agriculture, we're talking eons. Something tells me natural selection would have weeded that habit out (like it sadly might be doing with agriculture/grain consumption).
From a health standpoint, some veggies do not want to be eaten and contain anti-nutrients. Others offer their fruit as a tasty vehicle for spreading seeds. Deer comes by and eats a tomato, poops it out a mile away and there you've got a new tomato plant growing away from it's host. So it's hard to make a sweeping generalization about plants because different edible parts serve different purposes. A zucchini contains seeds and spinach leaves do not, they serve different purposes so they need to be taken as a case by case basis.
From a modern paleo standpoint, organic grassfed meat is friggin expensive. Veggies, especially this time of the year, are super cheap. We aren't talking about widespread negative effects like excessive carb and polyunsaturated fat intake, we're quibbling about details and individual nutrients in certain veggies. From my wallet's standpoint, I'm willing to tolerate that trade-off if I can get some otherwise nutritious and tasty food into my diet.
Doing a little research on how to best prepare each veggie takes some work but could settle some upset minds. Spinach's iron is best absorbed when it's cooked. Broccoli has its peak nutrition when its steamed. Do a little research and act accordingly. I personally eat a few salads a weeks and eat cooked veggies a few times a week as well. Mix it up, add in and swap out veggies. Eat them with meats and fats. Eating a well balanced diet is pretty sound advice, just avoid the food pyramid if you're curious which foods to include in that balance.