Real Tobin bronze shafting has been long gone for many years now and as such alloys in the stainless family such as Aqumet & Nitronic are now being used. These alloys, like type 304 and 316 SS can suffer from crevice corrosion. Crevice corrosion is worst when a stainless is in contact with seawater and also oxygen starved. This corrosion can happen between wet or leaking decks to chain plates or in keel stubs to the stainless keel bolts but many are unaware that it can happen to prop shafts too. Allowing the packing box to drip helps keep the water in the shaft log from becoming oxygen depleted.
Over the last 10-15 years there has been a dramatic rise in crevice corrosion of prop shafting. With the newer packing materials, and misleading advertising that use phrases like drip-less that cause DIY's to think it means "dripless" not drips less, owners have been starving the packing box area of oxygen by not allowing any fresh oxygenated water to pass through it. This can lead to the destruction of your prop shafting from crevice corrosion. While some packings such as Gore GFO, Ultra-X or GTU may be able to be adjusted to be mostly dry and still some what cool to the touch it is still a bad idea from a crevice corrosion stand point.
Another pit fall when a stuffing box is run totally sealed and "drip free" they can begin to trap air up in the shaft log. All it takes is a quick blast of reverse, and the resulting cavitation bubbles forced up and in, or after sailing in rough weather. Once enough air becomes trapped up in the shaft log the packing box you thought was cool to the touch begins cooking while you least expect it. Even PSS has now moved to selling all their dripless packing boxes with an air vent.
If a stuffing box is allowed to drip it allows for excellent cooling, longer shaft life, less opportunity for crevice corrosion and less opportunity for trapped air to run the box totally dry and cook it.