When i became a bit more experienced in TKD, i started switching my stance in MT. What i found is that, not only other fighters hate southpaws, but they hate it even more if you switch in the middle of the fight.
It's like they have to figure you out again from the start, and against a stance they don't like.
On the other hand, when i fight against a southpaw with a regular stance, i understand the base of his stance, and what i am supposed to do. So in my opinion, everybody should spend some time fighting as a SP to understand the logic behind it. Obviously with a trainer that will explain you the details.
Also, don't forget that against a southpaw, the liver is right there for the taking.
Blast him with switch kicks, and front leg teeps...
@TheBookofSpeed
In my opinion, its still a matter of both power and balance. It may not be as important as with a roundhouse, but the necessity it's still there.
Don't forget that the teep is not a front kick. It has a lot more power behind it that doesn't come from the snapping speed. You need the hand movement to help it.
Same goes for the balance part. Your hand helps counter balancing the rotation of the hips. Again, the hip movement is not as big as with the roundhouse, but it's still there, and it's a big factor on the power of the teep. So the hand movement is a big help for balance for that technique too.
I believe you can still have a decent teep and keep both hands up, (unlike with the roundhouse), but if you try it both ways you will clearly feel a difference.
Same goes with the piercing knee.
Again, don't forget that it's a basic strike, that is used constantly within a rule set that will punish low hands... There is a reason why it's done that way, and it's not hundred of years of laziness or bad technique...