I have always used only my right hand.
It all comes down to finding the correct angle. I have to admit that I cannot use the exact same angles on my right and left hand side.
On the right hand side of my face I hold the razor horizontally, on the left I hold it vertically.
but that has no effect on the shaving result.
I have never even considered using the left. Not because I don't want to, but becaues I never thought of it.
When going against the grain (if I want to be really smooth) I also use both sides of the razor.