You have already stated the biggest advantage that they have. That is the capability to be a coil-over shock. This, in itself, is a very big advantage.
Generally, they work by having several large holes through the piston. There are a corresponding number of rods (sometimes tubes) affixed to and protruding from, the end cap of the shock body. This is usually the end that is opposite the shaft end. The rods are of different lengths and sometimes tapered. The rods are made long enough to reach the piston and go through the holes at any position where enhanced damping is desired. These can be made so the rods are removable without disturbing the rest of the shock. This is usually done by threading the rods right through the end cap.
Some disadvantages include difficulty in "tuning", and lack of adequate flow, depending on how they are used. The rods must be changed by length and/or shape to change damping characteristics. There are no check valves other than those which can still be "squeezed" onto the piston. The flow is limited to whatever holes in the piston happen to be open at any given position. Generally, position sensitivity is gained but at the high cost of loosing speed sensitivity. External By-pass shocks do not give up their speed sensitivity because they still have valving on the piston and/or external valving can be spring loaded and not just a fixed orifice.
The internal By-pass shock does have possibilities and a distinct advantage. Someone just needs to come up with the right combination.