distributed systems are complex, and most likely you were bound to an overloaded webserver. My knowledge of S3 is six years old now, but the copy operation is single threaded with a tremendous amount of hashing to ensure durability.
At scale, the performance cost is worth it given the number of checks done internally to ensure the copy is perfect. If you download and upload, then you could make it faster however getting all the details right such that corruption didn't happen is tricky.
edit: just tried it, definitely seems to be working. not sure what I was seeing earlier, thanks!