It can help stop meat drying out during cooking, or add flavour to an otherwise cheap cut of meat - for example rolled neck of lamb with pistachio and sausagemeat stuffing, or belly pork with sage and onion stuffing. Yum yum
Problems arise when stuffed meats do not have the cooking times adjusted and the inside can still be raw. If timed properly it can be safe and delicious.
As an alternative to stuffing (which is very messy) I often stuff a quartered lemon or onion into the chicken, with a handful of fresh herbs like bay or thyme - flavours and keeps the moisture without the hazards of undercooking.