More reading on holding students back a year from the US perspective, with a slang term you might find interesting.
Sports is by no means always the reason, but it is indeed often a significant one. There are many American families for whom success in high school sports means more than all else, or for whom it represents the only chance at a scholarship to college. (Another concept largely alien to the German-speaking university system.)
But there are also other reasons, especially for boys. Not only sitting still and paying attention but also reading and writing are all skills that boys tend to develop a bit later on average, whether due to biology or culture or both. Academics are competitive too, and boys with a birthday near the cutoff whose parents opt to start them later may gain a slight advantage.
I would say it's a cultural trend in recent decades, though. The cycle can always swing back the other way, and parents who value academics may encourage kids to press forward rather than hold back. In my parents' generation and before, skipping a grade or starting early was seen as a mark of academic prowess. My dad, for instance, graduated at 16 and started college at a very sheltered 17 -- along with a lot of tough young WW2 vets in their mid-20s on the GI Bill who, so he used to say, corrupted his innocence with cigarettes and canasta.
Nowadays, with so many AP courses in high school, students who work above their grade level can often earn enough college credit to save them a semester or even a year of study at university. With tuition costs soaring, that could mean a lot less to pay on student loans, which in turn could mean being able to buy a house, etc.