Pretty sure I've seen some stats that playing your handedness side isn't really a big deal, it's far more important to just pick a side and stick to it. Guys who always play the right side will be better at it even if they're left handed than righty's who play the left and then switch to the right (as if there are any of those...)
Basically, don't flip flop a guy back and forth. Some players can learn the other side quickly and some can't, but basically no one can handle swapping back and forth.
Saw that a lot last year whenever AV tried to switch Holden back to the left side after he had been playing the right. He was always out of position because his instincts were to play to the right side of the ice.
Holden isn't a positionally sound defender... regardless of his side... you saw how exposed he was in the playoffs, missing checks and sticks.
Look no further than the devils v flyers in 2012. The devils owned them that series.
Flyers had 6 LH shots... so the devils kept dumping it in on the right side d, forcing the off-wing defender to pivot both ways with his back to the puck.. they then ran the 2-1-2 hard on that side...
It's a very claustrophobic position for that D, less time and space to make a decision with the puck... and lesser vision because he has to turn to chase the puck and look both ways... the flip clear off the back-hand isn't clean and leads to penalties.
Some guys are great at it... but this is what teams do on that off-side D.
There are nuances to the game that perhaps only the eye test can see... I'll give you another example...
Star forwards don't try a carried entry versus Karlsson... watch him play... they dump it... because when Karlsson turns... he does so at near the blueline against carries... no one can take it wide against him... so they dump it and force Erik to pick it up, and they try to win the board battle.
That's cause Karlsson, on his strong side, cuts the angle with speed and pins the entry on the wall... that prevents a play from being made. So the strong side option, with a smart and elite skater works well.
Nashville did it with their top 4 all playoffs... they shut down teams that way and counter transitioned. Against defenders like that, with the sticks lined up, it forces less controlled entries. Teams have to give up the puck and get it back.