The Joint Chiefs have no military authority, but are advisers to the POTUS.
It’s a side point, but setting up the Joint Chiefs was a good idea. But then having a Chairman of the Joint Chiefs was a very bad idea. As you noted, the Chiefs are just advisers. But having a chairman is a dangerous thing.
Better to keep all of them exactly equal.
The Joint Chiefs do, as heads of their various services. The Chairman does not.