Exactly, and in Europe the switch hasn’t nearly been as big. It’s becoming more rare, but you can still find SHL teams that sends out two Ds with their sticks pointing towards the middle at the same time (ie a LHS at RD along with a RHS at LD). When I played, this was seen as an offensive option (because Ds could pass D to D for a one timer) while the other way was the defending option.
But with today’s speed, it’s just especially those situations when you go and fetch a puck in the corner that gives you such a disadvantage if you play the wrong side. A RD on the right side will often turn and go back wards a little before they get to the puck to see the ice, then when they get there they can have their shoulder towards the ice if they fire the puck out. A LD in the same spot have to have the back towards the ice, and use a much weaker shot when clearing the puck. It’s just tough and gets to you if you have to do it year after year.