I, like many, have been on the search for the perfect veggie burger. And to my mind, there is a difference between "burgers" derived from a combination of legumes, grains, and/or fungus (ex. tofu, tempeh, and seitan) and "burgers" that are recognizably and predominately vegetables. In other words, there are burgers that qualify as vegetarian, and then there are vegetable burgers. It doesn't mean that these other foods can't be part of the mix. But when you rely too heavily on them, it stops feeling like you are showcasing the vegetables.
The problem is the lack of "chew." You know, the satisfying gets-stuck-in-your-teeth-like-grizzle experience that's hard to replicate without meat–and even harder if you bar the usual meat substitutes. And then there is the related problem of veggie burgers always falling apart.
So can it be done? For instance, I've tried incorporating shredded potatoes and carrots into the mix, trying to create a kind of mesh, but no dice.
Best Answer
Vegetables are mostly water. Water isn't chewy, protein is. What has a lot of protein in the vegetable world? Legumes, grains and fungi. Your "usual substitutes".
I feel like the requirements that you have laid out are self defeating.
Instead of not allowing the known chewy foods you should instead figure out how to use them for bulk and still showcase more flavorful vegetables.
I prefer white wheat that has been boiled until it bursts. Lots of texture but the flavor is easily overridden by whatever else is added.
As for a binder- the easiest is an egg if you don't need vegan. Otherwise you can use starch such as flour but you have to be gentle.