Very good. I too like the idea of being able to put the strong side forward. Better yet, the ability to fight well from either lead. The other day I was sparring a southpaw and he kept stepping on my lead (left) foot–I was fighting from an orthodox stance–so I switched my stance to southpaw and took away his tactic. Being more “squared up” e.g. in a Muay Thai style stance helps with that, also spend a lot of time shadow boxing in both stances to get comfortable. For me its all about taking my opponent out of his game and making him fight mine.
While training from both sides is a good idea, don’t try to use something you are uncomfortable with in combat. All techniques used in combat must be the ones you are best at, not the ones someone tells you that you should use cause “that’s what Bruce Lee, Ed Parker, or Chuck Noris used”