I was taught that the horizontal cut in the onion wasn't necessary because of the onions scale-like leaves. I can see this cut being necessary in a very fine mince. Opinions/reasons?

This is a very good observation and you are right if you are doing bigger cuts. The reason you ad the horizontal cut is mostly for the outer edges of the onion. If you don't make the horizontal cut, then when dicing, you will not get consistent dice. The pieces the come off the cut on the outside will be more like strips. Give it a try and see for yourself.

To be clear though, for large dice, you can skip this step altogether. Cheers, joe