I'm a lefty and my right hand is my dominant hand at the piano. I stare at my left hand the entire time I practice or play, even if it's just a repetitive motion. I was just playing around with Andante Spianato and was staring at my left hand even though it's the same 5 bars over and over without any jumps. I'm not sure if you play any other instruments, but I also play guitar (a left handed one). I picked up guitar 10 years after piano, and it accelerated my hand imbalance. Lots of stuff factors into it, not just which hand you write with (see rant below).
Over 2,500 left handed people die every year from using right handed products.
As a lefty, my life expectancy is 10 years less than a righty. There are a lot of interesting aspects of left-handedness. Strong correlations with premature birth and poor health at birth. Most of the blame goes to hypoxia (low oxygen). That is why I have epilepsy and most likely am a lefty. Of babies in the bottom 10% of birth weight, more than half ended up as lefties at age 4 from a study in '88. The human body is a strange beast.
"right handed products" that are deadly are things like chainsaws. The actual saw comes out on the right side of the tool, allowing a righty to stand away from it as you saw in case it kicks back, so you don't take your head off. As a lefty, anytime I use it I either have to hold it righty and therefore stand awkwardly, or hold it lefty with my neck sitting above the blade.
Why do I mention that? It's because "left-handed" is a terrible term in regards to issues like that. People that write with their left hand are left handed. What is the difference between playing soccer lefty/throwing a ball/snowboarding/using a chainsaw vs. writing left handed?
Balance. 95% of things that take a left vs. right decision process happen while you are standing, and it's about your natural tendency to balance.
Why the rant? a) I wanted to get a left-handed chainsaw for my woodworking stuff, and got lectured about how I should "just do it right-handed". Screw you guy that wants me to chop my leg or head off. b) There are very few people that do everything in life as a lefty and then write as a righty. Conversely, many people that write left-handed do things in life as a righty. It just drives me insane when I get told by fake lefties "I can do it, you can too".
/rant