+1
Not to punish her, but because the children deserve a chance at a full life.
He could've also either taken his own life afterwards, or turned himself in to the authorities. Hell, he could've at least admitted he had been drunk during the surgery.
Perhaps 'cowardly' is the wrong word. The entire movie has him trying to avoid taking responsibility, and in the end he sacrifices a member of his family in the most indirect way possible, still trying to avoid taking the responsibility of making a choice.
And afterwards (it's left unclear how they covered the death up) everyone tries to act like it never happened.
Even if he refused to sacrifice anyone, allowing them all to die in a f*cked up version of the trolley problem, it would've still been a choice. Leaving it to chance is his way of trying to avoid all responsibility.