Hi Haasome,
Efficiency of string energy to sound is determined by the degree of contact and the resonance of the material the string contacts. Assuming the bridge pin material doesn’t absorb energy the connection between string, pin and bridge will determine how well the vibration will transfer from string, to top to ear. Without a slot to encircle the string we’d allow an airspace that would compromise the transfer. Likewise if we only slotted the pin, OR the bridge, the unslotted component would not make total contact. The most complete contact is achieved by slotting each, pin and bridge with half the diameter of the string. If this is done to insure the string is encircled for the whole of its diameter, the most efficient transfer can be achieved.
An important exception is in the “do no harm” philosophy of the restoration of an historic instrument. Here a luthier is honor bound to maintain originality, without any discernable modifications that will devalue the piece. In old guitars you will find all combinations of slots and not.
All the best, Richard