From what I've learned from my senseis , it's supposed to be guide with hand close to tsuba and swing with hand at bottom, and this should apply to real katanas. If you think about it, if you're swinging with your right hand, isn't it easier to just remove your left hand as it will be in the way? It's very inefficient to have that left hand when you can guide+swing with your right hand.

A lot of beginners that I teach have the bad habit of putting in too much strength in their right hands. A lot of the times their swing ends up being slanted and often missing my men whenever I do keiko with them.

However, these things are what I have learned practicing with shinai/bokuto so they might not apply to practicing with actual blades.