Feeling a great deal about suffering and doing nothing about it are entirely compatible states. An hour of news can leave a person genuinely wrecked and no more use to anybody than before.
Compassion that stays as feeling turns heavy. It's also exhausting, and exhaustion is what makes people close the tab and stop looking at all.
What keeps it survivable is a narrow outlet — one street, one family, one Tuesday evening a month. Not because the wider suffering matters less, but because a feeling with somewhere to go behaves completely differently from one without.