Back in the days, most games with buttons (that I played) had them on both sides, others "joy left, buttons right", others "joy right, buttons left". Then 2 player games starting coming out, and most of them had the joystick left, buttons right, my preference. But a couple of my friends had to play the games arms crossed. One never "switched over", and stopped going to the arcades soon after (could have been growing up or something else, too). The other "switched over", but sometimes at a hard part of a "buttons right" machine, he'd cross arms until he passed that part. Haven't seen them for years, so don't know how they play (if they play) now.
Funny how most PC 'sticks (general & flight) with buttons off the stick have the buttons on the left. Complained to the companies about it since I was in college, and found out about the few "buttons right" sticks only after they were discontinued. Now, I'm a BYO, so I forgot looking for a "correct, buttons right" retail PC stick, and BMO!