"Counterfactual number of lives saved" is not the normal sense of the phrase "save a life". By that logic, each person's life can only be saved once, which is not how people normally use the phrase.

Your definition may be useful for cold hard utilitarian calculus, of the sort that hospital directors need to do if they've run out of fundraising opportunities. However, "effective altruism" – which I suspect you're alluding to here – isn't actually an efficient way to save lives, the way it's usually practised (ignoring second-order effects, and everything that doesn't fit on a spreadsheet).