When you say butterflies are bad pets, do you mean butterflies specifically or also moths?
I mean Lepidoptera in general. Moths aren't really any different because even though they fly at night, they need at least a little light to see. So if there is a tiny amount of light they will fly towards that. It's maybe not as pronounced as in butterflies and there are some exceptions. I found Hippotion celerio and Macroglossum stellatarum are exceptionally good at navigating in small spaces without hitting cage walls, etc.
I mean it's not a problem keeping Lepidoptera for generations and breed them but if you want pets as in "nice to look at when they fly around a big space" or like you have fish in an aquarium, that's not really what you can expect.
Do butterfly cages (...) help in keeping the butterflies from flying against the mesh, towards the light?
No, not really. They just provide a reasonably small space where they can find each other and their hostplants easier. That's not to say that in certain cases bigger spaces don't work. I know of people that had successful attempts of breeding some species in a greenhouse.
I believe the nectar mix is just honey water with a few minerals
I didn't know you can buy stuff like that. In America, I could see that, maybe for feeding hummingbirds but in Europe? You always find out new things...