OP, I have a strong opinion here formed from decades of living with pet rabbits. My pet bunnies are house pets, so I have the kind of relationship with them that most folks have with a dog or cat. BUT, they are not dogs and cats-- they do certainly have "rabbit-ness" that they express by running full-tilt through the house at 4 in the morning, nibbling on anything with a corner, playfully hopping away from me (we call this slow-hop game "chase the bunny"), pouncing on the cat, flopping dramatically in a patch of sunshine, carefully investigating any change in furniture arrangement. They love to be "bad" and do things that they are not supposed to do (I know that last is anthorpomorphization, but I haven't figured out what that behavior actually translates to in bunny terms. They clearly enjoy the playfulness of chewing something then dashing away from it when I enter the room). When they are happy, they jump in the air and do a "binky" like this: https://www.youtube.com/watch?v=NZgsMCRxXnI
In short, I don't think rabbits can express their true nature in a cage. They love to run. They love to jump in the air. They LOVE to explore new places. The key is, they will only do these things if they are in an environment that feels safe. Rabbits who live in cages turn into dull lumps, just like some people who are stuck in the same room all day (see the earlier mention of nursing homes and prisons, and how humans will sometimes choose to remain in confinement).
It worries me that most permies are very concerned with the happiness of their chickens and pigs, but don't seem aware that keeping a rabbit in a cage is limiting in many of the same ways.
For more info about what rabbits are like when they live in houses, see: http://rabbit.org/