I think 'authority' is a general perception which is a function of the music itself, volume level, headphones, extent and nature of our attention when listening, etc. IMO, it's fine to invoke the concept of authority to describe what we perceive, just as we use words like dynamic, energetic, clear, veiled, punchy, bright, distant, forward, etc. These words don't have precise meanings, but they help us communicate. And if an amp is truly underpowered, I can see that reducing the sense of 'authority' because dynamic range could be audibly compromised and audible distortion could be introduced. But if an amp has enough power, I don't see how another amp with more power could add authority.