It appears they don't log kickbacks because most of them are unreported. You only have to peruse fora such as this to see that kickbacks far outweigh finger and hand injuries. As you say some finger and hand injuries can be caused by kickback, I wonder how many hand injuries are caused by push sticks contacting the blade, they are an unstable and positively dangerous to use but I expect I am in the minority with that view though Jeremy Scmidt of YT fame certainly agrees with me and is very vocal on it in one of his videos.
The OSHA database includes kickback incidents if they result in an injury. If a kickback doesn't result in any injury that requires a trip to the hospital, obviously it doesn't get reported/recorded. You can browse the OSHA records one by one if you're interested in knowing how often it is mentioned as a cause for injuries (say, to the hand, eye, face, etc.). Same for the use of the push stick incorrectly.
The #1 reason for injuries (based on the first few pages of entries I've read) seems to be using the saw without the guard.
Forum discussions are NOT a reliable or valid source as a basis to say kickbacks happen more than finger and hand injuries. We should rely on official statistics collected or documented by hospitals or entities such as the OSHA.
Based on the info. collected by the US Consumer Products Safety Commission, about 10 table saw amputations happen every day in the States. Let's not downplay the role of finger-saving technology such as the SawStop and those advanced detection technology features on the sliding saws when we discuss table saw safety.
(One can find many examples of table saw injuries to the hand or fingers on the SawStop site. One can assume that most, if not all, of them (in the thousands according to SawStop) didn't require a treatment at a hospital, and hence don't get into any gov't injury data collection system.)