I think due to the shape and position of the lid, the pitchers are not meant to collect a lot of water, maybe just a little bit. I am pretty much sure the lid is meant to prevent rain from entering too much inside the pitcher. so I don't think they need any water in there. With some sarracenias, things are different, like with the purpurea. The lid seem to be designed to help the water go down the pitcher and those pitchers are almost always full of rain in nature. I don't know why it is different with different type of sarracenias.
When a pitcher gets too many insects, the mixture will rot and the pitcher become brown at that spot. Some people put something to block the pitcher after a few bugs, so that it does not rot. it does not affect the health of the plant though, only esthetic. With my seedlings, I fill them a lot with MaxSea fertilizer and they like it a lot. So either way they can do with or without water for most of them. If there is too much water inside, large pitchers can flip over.