As others have noted, the reason there are so many undetected stars in the milky way is because they are dim and very far away, so the light barely reaches us, or they're being occluded by clouds of gas and dust. Close-by stars do not have either of these factors. If they're dim, they're still very visible because they are close (Alpha Centauri and Bernard's Star) and there aren't any big clouds of gas and dust nearby that could be occluding close-by stars.