I'm a lefty and I shoot right. Growing up most of the other RHS I knew were lefties as well. Lefties are a minority in the population so that might be a factor.
I never minded being a RHS playing on the wrong side. In terms of using your body to cut a guy off or bump him off the puck, you dont have to turn yourself as much and you dont need to take that extra half second. Granted I never played at a high level though.
If you're as old as I am and started playing youth hockey in Canada in 1968, you've seen a big transition in this. When I was a kid, you most often shot with your dominant hand low. That meant the majority of right-handed people were right-handed shots and lefties were lefties. Note the word majority. If 10 percent of the population was left-handed, maybe 25-40 percent of hockey players in North America shot left-handed. A majority shot right-handed, but a number of right-handed people shot left-handed.
The tail end of that North American mindset has passed through the game. Steve Yzerman, Chris Chelios ... righties who shoot right-handed.
At the same time (60s and 70s), Europeans were predominantly of the opposite mindset. Right-handed people shot left-handed. Lefties shot right.
The best explanation I've heard came when I spoke with Johan Franzen ... When your dominant hand is low, you shoot harder. When your dominant hand is high, you handle the puck better. That explains the different views of the game between Canada and Europe in the 60s and 70s.
Now, 30-40 years later, the European mindset has clearly won out. It tough to find a right-handed shot who isn't a left-handed person. On the current Red Wings, only Chelios and Kirk Maltby fit that mode. Every other player on the team plays with his dominant hand high -- left-handers shooting right like Rafalski or Samuelsson and right-handers shooting left like Zetterberg or Lidstrom.
I think the ripple down to youth hockey is high, but I cannot speak to that. I imagine the majority of North American kids playing hockey now shoot left, which is the opposite of what it was 30-40 years ago.
This has definitely changed the game. The angles are obviously different. The mindset is different (stickhandling over shot power). The game will soon be played with 90 percent left-handed shots.
Forgive me for not remembering, but there was a Soviet team that came over -- 81 Canada Cup or 84 Canada Cup? -- that was 100 percent left-handed shots. That was still early enough in the transition of righties to left-handed shots in North America, that I remember the shock value when we saw that. We couldn't figure it out. Now, that's the way the game is played.