Setting the thrust on a rolling take-off allows a gentle acceleration - better for passenger comfort, rather than the sudden kick you get - more from oleo release than acceleration - when you release the brakes having set the thrust. So it's preferable.
However, as you suggest, you may for performance reasons need all the runway you can get. On our 45 tonne aircraft, if we're within 2 tonnes of the performance limited weight, or we're using full thrust for performance reasons (we don't normally to be kinder to the engines) then we do a standing start. The brakes aren't released until full thrust has been set and checked.
Lots of airline stuff is really black and white. If the book says you can go from a particular intersection on the runway and there isn't some other factor involved, then you can just go from there and not worry about it - no need to demand full runway length.