As with Korea, Vietnam, Gulf war, Afghanistan first time round, Iraq, Pakistan & Afghanistan again, the exit strategy is quite straightforward, extract the digit as sharp as possible once the fan can't rotate because of the accumulated sh*t.
The cost in lives is only a determining factor when...
Polls, polls, polls; I know they're the lens through which you selectively view the world in order to nourish your cognitive bias. I'm referring to real world, observed, natural human behaviour in response to a perceived threat.
That's probably because an immediate reaction is usually very visceral, fuelled by fear, anger and revenge that, for a majority of people, gives way to a more considered, big picture, rational response.