TL;DR: Quidditch is dangerous but most of the dangers are mitigated at Hogwarts and even if someone were to fall there are ways of making sure they stop or slow down enough that the impact isn't too harmful.
To start off with this answer mainly addresses things from the perspective of the books i.e. Hogwarts and not how things work in the professional world of the sport.
The main reason appears to be why injuries in more dangerous sports don't occur frequently in our more dangerous sports at schools in real life: the more dangerous parts are usually mitigated. Take rugby for example, at our school rucks were heavily monitored, scrums and lifts at the line out weren't introduced until later in school life i.e. when students were older. This appears to be the case at Hogwarts to as we see in this answer and the quote from it:
“Er — have the Bludgers ever killed anyone?” Harry asked, hoping he sounded offhand.
“Never at Hogwarts. We’ve had a couple of broken jaws but nothing worse than that. You don’t have to worry about the Quaffle or the Bludgers —”
In practice the role of the more dangerous players has been lowered to make the game more enjoyable for those involved and so it's easier to learn the sport.
To bring this around to why more people aren't killed well there is the Arresto Momentum incantation that slows or stops people as they are falling. According to the Lexicon it has been used during the 2014 Quidditch World Cup:
Used during the Quidditch World Cup 2014 by the referee in USA v Jamaica to stop Kquewanda Bailey from hitting the ground (Pm).
The Harry Potter Lexicon, Arresto Momentum
It is also most likely what Dumbledore used to stop Harry falling when the dementors attacked during a game.
"Dumbledore was really angry," Hermione said in a quaking voice. "I've never seen him like that before. He ran onto the field as You fell, waved his wand, and you sort of slowed down before you hit the ground. Then he whirled his wand at the dementors. Shot silver stuff at them. They left the stadium right away... He was furious they'd come onto the grounds. We heard him --"
Harry Potter and the Prisoner of Azkaban, Chapter 9, "Grim Defeat"
It appears to have been what Hermione uses when the group are in Gringotts as they fall though that is only mentioned as the Cushioning Charm. Therefore, it is very likely that most, if not all, falls can have their effects mitigated in games of Quidditch where there are a lot of Wizards present.
In some of the bigger tournaments there are even mediwizards on stand by to help out injured players should they need too.
“It’s time-out!” yelled Bagman’s voice, “as trained mediwizards hurry onto the field to examine Aidan Lynch!”
Harry Potter and the Goblet of Fire, Chapter 8, "The Quidditch World Cup"