Leonardo's weapon of choice, the katana, explains why he's the greatest leader of the Splinter seems to have chosen the Turtles' weapons carefully, rightly realizing their opponents would struggle to adapt to a group who used such diverse weapons and tactics.
The Turtles' greatest leader is Leonardo, and he's a force to be reckoned with courtesy of his twin katana. These ancient blades were mainly used by the samurai, the military nobility of Japan, and they're generally seen as the best swords of all time. This is largely because of the way the katana is forged, which gives it impressive durability. Meanwhile, the reach is particularly impressive; the katana is long enough to deal with more distanced opponents but short enough to be effective in close quarters as well.
There's a sense in which the katana is also the secret to Leonardo's leadership of the TMNT. The katana is a quick, reactive weapon, and its wielder must learn to respond to threats in an instant - with next to no thought-time. Like many strategists, Leonardo tends to overthink and overanalyze; the katana forces his mind to process at a much faster rate, to strategize based on incomplete information rather than to become paralyzed by the unexpected. It's the perfect weapon for a leader like Leonardo, and his training serves as a mental discipline.
Of course, Leonardo has had to adapt to traditional katana techniques. He holsters them on the back of his shell rather than in his belt, meaning he doesn't draw them in the same way as a samurai; many characteristic katana strikes are based on that swift draw, so Leonardo has to switch things up. What's more, like his brothers Leonardo only has three fingers, meaning he needs to change his grip a little. Those fingers are also thicker than human ones, likely meaning his grip is a little stronger than the human norm - giving him an advantage in battle.
Though some would argue that Leonardo and Raphael should switch weapons, it's clear that the katana is truly perfect for a leader like Leo. The interesting question is whether Leonardo's training with the katana has ever conflicted with his temperament; whether he's ever struck at speed, and then found himself second-guessing his decisions a moment later. Presumably this, too, was an aspect of Splinter's training, with Leonardo's sensei encouraging his student to live in the moment rather than to become distracted with the past. Such an approach will be key to ensuring Leonardo really does fulfill his potential as the Teenage Mutant Ninja Turtles' greatest field leader - and the champion of the katana blades.
