Because we have an opt-out system, the vast majority of people choose to donate their organs. About 73% of people will donate their organs. As opposed to the US, where only about 54% decide to donate. I think there's a meaningful difference between those circumstances.

Not to mention that "only 3 in 1,000 people die in a way that allows for deceased organ donation". Which makes the chance of me personally being responsible for someone not being able to be helped very small.

So the problem is more a matter of how people die than how many people donate.