Many karate styles can be titled as "sport". Shotokan is one type of school who embraces their form of kumite, as well as many japanese goju schools, and from what I have seen, many old style traditional schools as well. Kyokushin just has a different version to express their liveness and other attributes that are built against a resisting opponent. Many Kyokushin schools still do kata, and bunkai, and last I checked (last night actually) we are still doing knifehand attack drills aimed to the neck area, low sidekicks to the knee, hooks (forgot the name of the strike, but its not a hook) to the back of the neck, backfists to the bridge of the nose. Its all in the syllabus.
Just because the actual fight of kyokushin sparring is what stands out, doesnt mean its the end all be all.
And frankly, after having to fight 10 people being recycled back to back with no rest period with or without protective gear taught me a whole lot about self defense. Because from my experience, a low kick is still a low kick, a punch is still a punch, a dodge is still a dodge, and we throw them at full force as legally allowed with as much minimal equipment possible, and at black belt with no equipment. Its pressure testing, body conditioning, and full force application, mind you against other fighters who at the same or even above level as your own.
And for the comment of kicking to the groin and neck, what style does that? Someone can easily argue that hitting thin air, or stopping inches to these areas from prearranged fighting, isnt exactly performing kicks to the groin and neck.