I don't think Amazon wants to remind people it is omnipresent like that.
For example, I got an Amazon Tap because I liked having a physical button to enable the mic. They then released a setting in the Alexa app that allowed it to always listen when toggled on (yes, I realize if I truly cared about privacy that a button like that is just an illusion and they can record whenever they want).
That was fine, I tried it out in situations where I didn't have a free hand (doing dishes for example). It had red notification lights that came on when it was always listening which reminded me the setting was on. This is also important because of the way the battery drains when it is on.
Recently I went to switch it on, and no red lights. There was no visible indicator my Tap was listening or not.
Better yet, they should put a stepper motor in the bottom of the unit. Then it can rotate towards the user. That would work better for hands-free use, and would make the video calling work better too, if you are up and about.
I'm surprised an Amazon Echo accessories category hasn't really started yet. I could see kids loving a pair of googly eyes on their family Amazon device 8-)
Seriously, these boxes should have a pair of eyes drawn on them as part of the design, to remind the user that they are being watched.