I think that a well-written and/or a well-run game can push a ton of emotional buttons. But the majority of games I’ve been in – the vast majority of games – when things started to get too intense for the characters, players often insulate themselves from their characters to avoid letting character emotion drive the player.
It’s an easy shift to spot as GM, too – players shift from first-person to third-person when describing character actions when they’re trying to step back.