One hand on the yoke and the other doing nothing, unless you're on the Airbus just looks gash...why would you ? I mean what the f**k do you really want to use the other hand for?.
Back when airlines flew the DC3 long before the jets were in service we kept the other hand on the throttles until a positive rate of climb was established after which the PNF would take control of the throttles for the first power reduction.
An engine failure at the wrong time can result in yaw towards the failed engine and if the pilot flying has both hands on the wheel you have two pilots trying to control yaw.......much more simple for the pilot flying to be in complete control of the airplane.
That method worked quite well for me during the over five thousand hours I flew the DC3....
......never ever lost control of one doing it that way.