Aunty and Fishbelly you got it right.
I was started with a spinning reel left and rod on the right and I am a left handed person.
I fished this way for years because my father is right handed.
When I first start using a baitcaster, I swear to be a true left hander by holding the rod on the left and reel on the right.
I refused to switch hand while learning to handle this new setup.
Now I have both left reel and right reel to use on a long trip to balance out both arms from fatique. And I don't ever do the switching hands either way.

I suppose those people who are doing the goofy swithing hands were brought up on an era where there was no left handed reels.
This is the only logical explaination. Sure is funny watching some of them cast, set he hook, and fighting the fish. They had to be magicians for switching hand so fast in 3 motions.