In the 25th century there're hundreds of descendants of Superman and Supergirl living in Earth. In the 31st century, though, there's only one member of the House of El alive, Laurel Kent. Apparently, the great confrontation between both sides of the Family was bloody.
Why Supergirl's costume isn't inherited unlike Superman's? Because Superman only wore one costume, ever. Supergirl's classic costume (long-sleeved blue blouse and red skirt, boots and cape) is iconic, but Pre-Crisis Kara Zor-El easily wore one dozen of costumes and at least three of them are considered emblematic for a particular decade.