Punkoinyc: I'm kind of surprised that controllers designed for left handed people aren't commonplace.
By "controllers", what exactly do you mean? Flight sticks? Gamepads?
Flight sticks are not really that popular anymore (outside some classic PC gamers, like many people here), but I recall some flight sticks were suitable for both hands, ie. they were symmetrical in design.
Gamepads... aren't they just as good for left and right handed people? You need to use your both hands with them anyway. I'm sure there are lots of left-handed console gamers using the gamepads just fine.
Overall, it is quite normal you have to use both of your hands anyway. Even if one of your hands is operating a mouse or a flightstick, the other has to operate the keyboard at the same time anyway. Heck, I even recall playing Mechwarrior 2 with both a flightstick and a mouse at the same time (mouse was in my left hand, a symmetrical mouse like most mice are).
Not to mention that the "fighting arcade sticks" usually had the opposite configuration, ie. the stick is in your left hand, and you operate the buttons with the right hand. I am unsure if Japanese are mostly left-handed, or why that is. It did take me some time to adjust because on PC I was accustomed to the opposite (a stick in my right hand, operating the keys (the keyboard) with my left hand).
https://www.google.fi/search?q=arcade+stick&biw=1280&bih=837&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwiDyqj_89zPAhUqMJoKHS85DDwQsAQIMA