I'm left-eye dominant and shoot right handed. I shoot instinctively so I don't consciously have any awareness of the bow/arrow location. My focus is on the "spot." If I do look at the bow/arrow position at full draw, I see nothing that helps my shooting. I don't care because I want my focus to fully on the target. So then, does the bow/arrow location help me get on target? I'd say my brain has finally figured it out and the answer is yes. But since I shoot instinctively, with no conscious aiming reference, it matters not.
So, if you want to shoot instinctively and you are in more control shooting right handed, I would not make the switch. If, on the other hand, you think you might want to tinker with gap shooting etc., then you will have to make the switch.
For me, fun means keeping my focus on the target and letting the arrows fly to the mark. I don't want to think about anything on my end of the equation. For others, fun means taking more control at their end of the equation and manipulating variables to figure this out or that out. Once you answer what kind of person you are, and both are absolutely okay, you have your answer about switching. Hope that helps some.