One of the most incredible and memorable fights in Classic Naruto was Kakashi against Zabuza. The end of the duel, as you know, resulted in Team 7 being victorious. But, after all, why didn’t Kakashi take Zabuza’s sword for himself after defeating the enemy?
First of all, Zabuza’s sword was one of the Seven Swords of the Mist and therefore belonged to the Hidden Mist Village. At the time of the fight, Leaf and Mist were enemies and, for that reason, if Kakashi got hold of a valuable asset from Mist, there was a chance of a war between both villages.
In addition, it is worth remembering that Zabuza’s sword was made of solid metal and, therefore, was very heavy. Momochi could only wield the sword masterfully because he had trained a lot with it before. And even though he was a well-trained ninja with the weapon, Zabuza had to drop the sword at times during the fight to preserve his energy.
For that reason, Kakashi preferred to use the sword as a tombstone for Zabuza, instead of taking possession of it. Finally, it is worth remembering that Kakashi is a ninja assassin, that is, he needs to be precise and fast while moving. The sword would make him less agile, which would consequently decrease his chances of victory.