I can't speak for the parent, but my feeling about it is that I don't like food
pretending to be other food. So yes, serve me up a mushroom burger or a falafel burger, or a winter black bean and kale burger. But if the menu says simply "veggie burger" then there's a pretty good sign that it's an imitation and not made from whole food.
Now, none of this is implying that the veggie meal should be a "bland plate of veggies", rather it's that there are whole cuisines out there with delicious plant-based meals that have stood the test of time. If I'm eating vegetarian, I want one of those meals, not a meat meal with the meat swapped out.