Yes, and what exactly is "the judicial Power"? Roberts, C.J., famously said that it was that of an umpire calling balls and strikes.
As a far-fetched analogy, Chevron deference is a bit like having a committee of uninvolved players and managers determining where the strike zone will be for each ballpark. If the team owners agree on such a meta-rule, then the umpires need to call balls and strikes based on that meta-rule, using the strike zones determined by the committee. It's not up to the umpires to decide that the owners can't delegate that authority to the committee.
As a far-fetched analogy, Chevron deference is a bit like having a committee of uninvolved players and managers determining where the strike zone will be for each ballpark. If the team owners agree on such a meta-rule, then the umpires need to call balls and strikes based on that meta-rule, using the strike zones determined by the committee. It's not up to the umpires to decide that the owners can't delegate that authority to the committee.