Marchand-Bergeron-Recchi
Chara-Seidenberg
Wow, I totally forgot Boston won the cup 2 years ago. But yeah, that's their most important forward line and their most important defensive pairing.
Whether the proper side thing was responsible for Ovechkin's renaissance or whether it was something else, like coach's confidence or just working through a slump, is up for debate. He still scores a lion's share of his goals from the left, especially on the PP. And even if you concede that it did help Ovechkin (and I'm fine with keeping him there since it's working) it doesn't mean it's going to help other players playing other styles. Not every player in the league is Brett Hull. Here is just a list of some players who played most if not all of their careers on their off-wing aside from Ovechkin - Jagr, Bure, Recchi, Shanahan, St. Louis, Kane/Sharp/Hossa, Havlat, Gaborik, Lupul, Nash, Vanek. Also Heatley and Kovalchuk. I could probably think of a lot more. Having no one playing on their weak side means you make it significantly harder to cut to the middle and make plays from doing that, which is a huge part of any team's arsenal. You pretty much have to grind your way in from the outside along the boards.
I'm not familiar with baseball but I'd be wary of any arguments from a sport whose resemblances to hockey are metaphorical at best.