Cosmic Encounter, Jump Drive, Heroscape, Sagrada, Azul, Sushi Go Party, Kingdomino off the top of my head

Except the fringe case was a meta card since it was released, and the point of it placing damage counters is to get around certain abilities. It's an intended mechanic to add more depth to the game.

It's because placing damage counters interacts with some abilities differently than dealing damage.