Yes, Include Lefties
No, Righties Only!
What if I told you that the characters are right handed because it puts the gun on the right side of the screen. Unless you're in Japan, your eyes are naturally trained to pick up information left to right. The gun blocks a lot of space, and the eyes searching for enemies has a more difficult time reading around it. The screen has an overall higher readability by showing the information that is easier for the viewer to take in first before making them search around an object. Searching around an object first slows down the entire cognative process. Even if the option was there, you'd find yourself worse off for doing it...