The problem isn't greens, it's the type of greens and the amounts most people are feeding. When you look at the diets of wild rabbits, you'll find that they tend to eat a lot of really dry roughage...branches, weeds, etc. They don't come across the types of nutrient-dense, watery (and sometimes sugary) vegetables that HRS recommends.
I agree that balance is key and the balance I've found to work the best is, well, mostly hay! Like...ridiculous amounts of it

. Then my bunny gets a decent helping of "drier" (sorry, sleepy...can't think of a better way to describe them, ha) roughage/herbs as opposed to watery vegetables...lavendar branches, birch twigs and leaves, willow, rosemary, basil, oregano, mint, parsley, clovers, garlic mustard, wood sorrel, fresh grasses, apple twigs, and whatever weeds I notice are being nibbled on outside (only do this if you at least can ID any poisonous plants). Then, before bed, he gets a
small traditional salad. He'll get a couple of the following: romaine lettuce, escarole, kale, spinach, chickory, red/green leaf lettuce, and carrot tops. For treats he gets flowers (whole or petals), dehydrated greens (like the Green Crunch from the Bunspace store or homemade), and the occasional small piece of fruit or a more watery/sugary vegetable (carrot, celery, cucumber, bell pepper, etc.).
I, like you, began questioning the HRS-type diet (nothing against them, though, it's a step in the right direction!). After studying the anatomy and physiology of wild rabbits, I knew pellets couldn't be good. But looking at their wild diets, the kinds of vegetables/fruits recommended didn't seem "right" either...at least not as a pellet substitute in the amounts recommended.
Then I thought about the times I had brought out my rabbits to play outside. I thought about how I would watch them "foraging" and picking out weeds and flowers to eat. Why not feed them weeds and grasses from outside? It seemed more natural and they would be getting a good rotation of plants depending on the season. And then I found out that some people, who raise outdoor rabbits in pens, don't bother with pellets at all. The rabbits live on the same kinds of things they'd eat as wild rabbits. And they're totally healthy! I also discovered, though research (and trial and error), that herbs tended to sit better with rabbits than more watery veggies like, say, celery or bell peppers. So I began feeding more herbs, in addition to the wild plants. Actual vegetables were decreased, pellets were eliminated, and both fruit and grains were almost completely removed (I still use fruit as bribery sometimes, ha).
I want to do a bigger research project on rabbit diets but that's not exactly my field (marine biology, haha). There's no money in a project like that, anyway. So all I can offer are anecdotes...like my 10+ year old rabbit suddenly gaining energy and muscle mass back on his new diet. And how now he can keep weight on. I was considering euthanizing him at one point when he was doing especially bad (a couple years ago) so this is a big deal to me

. This diet has also done wonders for my foster rabbits so it's not just Elvis.
I don't think any one diet is "perfect". But I think both pelleted diets and vegetable-heavy diets both need some tweaking. I also think most rabbits aren't getting enough dry roughage (such as not enough hay, but I think we can agree there), including branches/twigs. Twigs/bark make up an important part of a wild rabbit's diet, especially in winter, yet are ignored by most diet plans.