Not to flog a dead horse here or argue for the sake of arguing, but tennis is definitely one of the sports where early specialization is beneficial. Yes they may have played other sports as well, but the point is they started playing tennis at a young age and focused mostly on that. Let's look at the big 3 (source wiki)
Federer also credits his hand-eye coordination to the wide range of sports he played as a child, including badminton and basketball. Federer played his first junior match in 1996 at the age of 14 at a grade 2 tournament in Switzerland.
As a young child, Djokovic was given a mini-racket and a soft foam ball, by his parents, which his father claimed, became "the most beloved toy in his life". Djokovic began playing tennis at the age of four, when his parents sent him to a tennis camp in Novi Sad, as his parents had not played any tennis in the past. In the summer of 1993, before attending primary school, the six-year-old was sent to a tennis camp organized by the Teniski Klub Partizan and overseen by Yugoslav tennis player Jelena Genčić, at Mount Kopaonik, where Djokovic's parents ran a fast-food parlour and a sports equipment business. Upon seeing the child Djokovic playing tennis, she stated: "This is the greatest talent I have seen since Monica Seles.
Recognizing in Rafael a natural talent, another uncle, Toni Nadal, a tennis coach, introduced him to the game when he was three years old. At age 8, Nadal won an under-12 regional tennis championship at a time when he was also a promising football player. This made Toni Nadal intensify training, and it was at that time that his uncle encouraged Nadal to play left-handed for a natural advantage on the tennis court, after studying Nadal's then two-handed forehand stroke. At age 12, Nadal won the Spanish and European tennis titles in his age group, while also playing football. Nadal's father made him choose between football and tennis so that his schoolwork would not deteriorate entirely. Nadal said: "I chose tennis. Football had to stop straight away."