Short answer: If you enjoyed it, don't question the logic.
This is an example of Artistic License, which means the author is allowed to ignore logic if it makes the story more enjoyable. The trope of a character's ability extending to their equipment is known as My Suit Is Also Super on tvtropes.1
Cloning techniques in Naruto require this trope due to how it is usually used: to confuse, distract and deceive the opponent. Cloning based techniques would be useless if the opponent could tell the original apart from the clones by simply looking at who has a shuriken in hand!2
Artistic License requires Willing Suspension of Disbelief from the audience. This is acceptable to the audience since they want the story to entertain, and do not necessarily want it to be logically accurate. The author should maintain a balance between the Artistic License and the Willing Suspension of Disbelief that the audience is willing to give.
If he uses too much Artistic License, the audience cannot take him seriously anymore. For example, if Naruto had awakened Mangekyou Sharingan, and it was explained with "an Uzumaki can awaken Mangekyou Sharingan by repeatedly using Shadow Clones and Rasengan", then the audience will lose interest in the story.
It he uses too little of it, an opportunity to make the story more entertaining is lost. The author would have had to exclude a lot of techniques and events from the story, which would make it too boring.
1 The trope of cloning techniques extending to the user's clothes is Magic Pants is used mainly for censorship reasons, as otherwise the clones would end up naked. It is too much trouble for the author to keep dealing with all the time. Given how often the cloning techniques are used in the story, it would also get annoying for the audience after a while.
2 Interestingly, in a much later battle, Kishimoto plays with this trope differently. Naruto makes one of his clones carry a certain thing which fools his opponent into thinking that clone is the original. See the below spoiler for details.
During the battle against Kaguya Otsutsuki, Naruto deliberately places the Gudodama behind the back of one of his clones, which tricks Black Zetsu into thinking that clone is the original.