Many herbivores have a part of the digestive tract devoted to fermentation (or other microbe based processes) to break down cellulose. This involves a community of microorganisms that live in that part of the gut, and it is those microorganisms that break down the plant matter, producing nutrition for the animal via the products of their digestion, or by the animal breaking down the microorganisms themselves. Ruminants in particular like cows with their specialized multi-compartment stomach devote a lot of space to culturing this microbe colony, but rabbits and horses are hind gut fermenters so they have cecum for that. Rabbits also are coprophagic (eat poop), they digest some of their plant matter once, then eat the poop pellet and send it through again so it can be broken down even more.

But basically, with the microbes doing the work of digestion, it is more about what they can extract, and the herbivores just host them. We have a different community of microorganisms than them, and our digestive tract wouldn’t be able to support large numbers of those species.

It's a bit of both. Diet, volume and biology.

Humans mostly absorb iron through the duodenum, which is a very short bit of intestine near the stomach.

Herbivores, on the other hand, have either massively complex systems of stomachs, chew their cud to make nutrients more absorbable, or letting food ferment before digesting. The latter also works for humans, if you like fermented veggies.

Of course, diet also matters. Humans don't eat all that high iron foods, but grass is a cow's main food source and it's high in iron.

This is going to cover the factors that affect the ability of humans to absorb Iron which isnt quite addressing your question directly but I would rather not speculate about things that I have not researched as thoroughly. Iron bioavailability depends on several factors including what you eat along with the Iron. Citric acid and protein significantly increase the bioavailability of Iron. Plant foods rich in phytate (what plants use to store Phosphorus) bind to and render unavailable metals like Iron, Zinc, Calcium etc but these levels vary significantly between plant food sources. Other metals like Zinc can interfere with Iron bioavailability and vice versa. And normally the body's ability to absorb Iron is regulated such that Iron is absorbed more efficiently if you are deficient and less efficiently if you have an excess. There are a few disorders that cause this Iron regulation to malfunction either resulting in deficiencies or the complete opposite of this, excessive Iron that starts depositing in organs but with a physiologically "normal" person that regulatory system acts to normalize the amount of Iron absorbed to an extent.

Humans are omnivores for a reason.

I would argue it is a feature and not a bug. Your body controls the uptake of iron with hormones. Those hormones work less effectively on the uptake of heme, but I would say that is the bug. Hemochromatosis (abundance of iron) can present the same symptoms as iron deficiency. Both issues are usually caused by genetic issues rather than dietary ones though.

Are we actually that bad at absorbing iron? Honest question, I always assumed it was a matter of the amount of iron in there in the first place.