There is much more to this than just hands. A very long time ago I really offended a biology prof. He was happy to think there were people with no hand dominance, but could not accept a lack of eye dominance, he couldn't imagine how that could be. I had just spent two years going through paper journals reading about dominance, before there was the internet. A substantial number of left handed people lack eye dominance and some other things. Fun experiment. Get a paper plate, cut about an inch round hole in the middle. Ask some right handed and some left handed people to hold the plate at arms length to look through the hole at something across the room and then keep looking at that as they bring the plate up to their face. Almost all the right handed people will automatically do this and not understand what the point is. A substantial number of the left handed people will move the plate part way and then hesitate and shift the plate back and forth. Some will finally obviously give up and just pick one eye. That is because they have partial or even total lack of eye dominance. Left handed people to some degree see the world differently. Nobody has ever brought it up and they just think that is the way everyone is, just like right handed people think. Supposedly before birth there is a major shift and reorganization of brain function and for left handed people some of that shift is incomplete. I suspect with some thought and just the right experiments it would be possible to find surprising differences. Remember, there aren't many of us, but we are sinister.
"If you're left-handed, this does not feel natural, and so left-handed people usually end up writing backwards."
I'm a lefty, and I do not believe this is remotely true.