I understand what you mean about the caged animals - we have 2 rabbits, 1 guinea pig (had 2 up until last year), 2 cats and 2 dogs, and the rabbits and GP are the most difficult. We didn't even set out to have them - our first rabbit was a pity case. She was 4 months old when I saw her in a little pet shop I'd popped into on my way home, and was in a tiny glass tank that she could hardly move in. There was a sign stuck to the glass saying 'Free rabbit, must go this week, on death row!' like it was some joke. Horrible man grrr (business went down the pan a few months later, that's karma for you!). I couldn't leave her there, so instead of some cat litter I left with a beautiful black long-haired lionhead rabbit in a box! It was my birthday though (and t'was fate, obviously!), so DH couldn't shout A few weeks later, when the outdoor 'rabbit mansion' was finally built, we got her a companion - a dwarf lionhead rabbit, or so we thought. He just kept growing and growing, and is now almost 5kg and twice the size of her! But then again, he was also supposed to be a 'she', so what did we expect?! The guinea pigs belonged to our neices, but one of them became allergic so they had to go, and we agreed to take them so the girls could still visit. So then there were four!
As much as I love them, I wouldn't have caged animals again. I used to have a horse and I would almost put them on par with that commitment wise - cleaning out daily, fresh greens every morning, fresh hay and water twice a day, checking them morning and night, cold proofing in winter, heat proofing in summer, exercising, nail trimming, grooming etc etc - and it's impossible to get someone to look after them when you go away. Actually, scratch that, I could always get someone on the yard to look after the horse - rabbits are harder! And, as lovely as they are, you just don't get much back from them like you do with dogs or horses.
I think a lot of people underestimate the amount of space and care rabbits need, and think they're the ideal pets. When someone asks me for an easy pet, I say get a cat - or a goldfish!