Why do most rotary potentiometers have an opening?
I think it is to do with manufacturing process. Most low cost pots have a carbon track that has been deposited onto some kind of fibre board, which the wiper mechanism and cover attach onto. They are designed to be cheap and easy to put together. You can also get sealed pots, but they cost several times more:

10k standard pot

10k sealed pot

The gap is handy for squirting cleaning fluid into, though.