When I first started school back in the early '70's, they MADE you write right handed. It wasn't until I got to the 3rd grade that I was falling so far behind that I switched to my left because it felt more natural to me. Since I had been writing right handed for a few years, I made the switch with no difference at all to my alignment because I had already memorized the letters.
Most left handers that start out left handed from the beginning do "the claw" so that they can see what they're writing as they write it. It's how they learn. I didn't have to see what I was writing because I already knew all the movements, I simply had to get the pattern down in reverse.
One of my neat tricks is writing on the black board with both hands at the same time. I can even do it in two different languages (English and German) with simple statements.