I don't think he copied chidori that was taught to him he learn to do it himself. And yea original moves are cool or what ever but having other jutsus that you could use are always useful.He copied Chidori. Plus, why would he need to copy? Wouldn't it be better to have your own set of original jutsus so no one would know about it?
Lets say Kakashi never had his water wall, Itachi would have killed him, so just having jutsus as a backup even if you don't use them often is useful.