Not quite that simple.
If you have TO-1 or TO-2 selected for take off you must not select TOGA as you will exceed these thrust settings and so bust your VMCA calc. Also the same if you manually advance thrust levers beyond the assumed temp limit and as this is not indicated its easy to do.
Why would you want to go for TOGA with single engine as you have adequate performance without as per the legal requirements ?
We have a nice feature where the EOsids (emergency turns) are all in the FMC and auto pop up on the map when an eng fail is detected. All you do is execute and continue with LNAV at 50ft.