Going back to the original question.
I've now tried the scenario in the sim and to keep the engine running on the approach seems to me to be the more risky option. I'm not saying it can't physically be done, but it's definitely more "seat-of-the-pants", and results in a much less stable approach than with one engine shut down.
Sure, keep it running if you've still a long transit to make, but in my opinion it should be shut down in preparation for the approach.
Why?
1.) Because even with flap 40 and the other engine at idle, the speed still wants to run away. This should not be overlooked as a minor inconvenience. It presents a fairly major handling problem. It may be necessary to exceed flap limiting speeds and use speedbrake with flaps at very low level to control the speed.
2.) Now we're making a flap 40 approach, yet we don't have full thrust available for the go-around.
3.) Rudder pedal inputs need considerable attention as they are not what we are used to single engine.
4.) It's not easy to get the aircraft on to the ground in the flare with 77% still pushing away and some excess speed as well. Runway then gets eaten up as the engine (will it be the correct one) is shut down.
5.) All the above requires the aircraft to be operated in a totally non standard manner.
The idea of "experimenting" in free airspace is fine if we have a truly serious control problem. However, all we actually need to do is shut the engine down when ready for the approach, and we can then fly the aircraft within the SOP's as we are trained to do, hopefully in a calm and stable manner to an uneventful landing. I know which one I'd go for.