I've wondered about that myself. As a 'Chunner, I keep my shoulders square to my opponent when in a medium to close punching range. But in Eskrima I tend towards "power-side forward". Our stance and alignment is very similar to JKD: right arm and foot lead, body "bladed" sideways, weighting either about 50-50 or 60-40 favoring the front with jabs and power punches coming off the lead arm.
Since Filipino martial arts typically start off with weapons such as sticks, this orientation makes sense. You want your baston in your power hand and held forward to attack and defend. Sure, with empty hands you can switch to a conventional stance, but I've gotten so used to a power-side lead, that I prefer it with or without weapons.
As for how this works with my WC, --well I usually assume athe "JKD-ish" looking Eskrima stance at longer range, especially if I'm holding a weapon, and merge into a WC stance and strategy as I close range -- at least when empty handed.
Now back to the original question: Not being a boxer, I really don't know about the advantages of conventional vs. southpaw stance. Part of the question depends on if you are armed or not. Another part may depend on your objective, whether it's self defense or sport competition. In sport, the laboratory of the ring seems to favor a conventional orientation, at least for right-handed boxers. However in self defense where you can reasonably assume that your attacker will have a physical advantage over you, there may be more value in fighting off your power-side, starting with all you've got, in order to end it quickly and escape.