Some recurves have sights. It's still not uncommon.

Hunters have killed every game animal on the planet with longbow or recurve, and still do, including elephant and Cape buffalo.

Accuracy isn't in the bow, it's in the archer. Those dedicated enough can become deadly accurate at long distances. The best compound bowhunter I know shoots without sights, and does very well. He's a good hunter as well as a good shot.

Short answer, if you want to learn to shoot without sights, it's not that hard. Get good instructions and practice.