I've been thinking a bit about this one. For me, it depends. It depends on what I'm trying to achieve.
A maintenance enclosure outside, used for adults, might be open topped to allow air to circulate and to prevent the likelihood of mould (due to for example uneaten segments of worms etc). Stick your nose in....is the air stale? That's a big no no. I also believe a bit of sunshine helps keep micro organisms at bay (I'm thinking uv). It also keeps the humidity and temperature similar to the outside surroundings which is important when I'm priming adults for next year's breeding.
Enclosure siting is important too. None are placed in deep and prolonged shade or full and prolonged sunlight.
Come the winter though, then a wooden lid is placed over them on cold days to take the bite out of sharp frosts. I am also conscious of excess rain and wafer logging. Allowances are made for drainage but on particularly prolonged periods of rain then a polycarbonate lid is put over.
Growing on youngsters have a similar set up but I never leave the enclosure uncovered. I've seen birds flicking through the leaf litter in the enclosures and won't run the risk of losing any youngsters. I also find that these youngsters are more agile than the adults and maybe could escape by crawling up the walls. A wet belly certainly helps them stick to the sides. Yes, all enclosures do have over hangs but I won't take the risk.
Enclosures inside are nearly always covered. This might be with a glass sheet with a 1 or 2 mm screen (size to prevent 2+ instar crickets from escaping) on one end only. This ensures a humidity gradient (I've used a hygrometer). Obviously the type of substrate and positioning of a water container have a big influence here and this is where knowledge of the subspecies' habitat comes in and what you're trying to achieve. These indoor enclosures are really for my yearlings which I want fully active and feeding.
There are times I will mist the enclosure to increase humidity and water dropletsavailability for the animals and will leave the screwing covered for an hour or so. Other times I will remove the glass plate to allow a certain amount of drying.
For me, it seems to be working but I'm always conscious that I have much to learn and my system will evolve accordingly.