Google and Amazon are huge companies and would face serious liability for falsely advertising that their devices only listened upon hearing the wake word. Moreover, I'm sure someone out there would analyze the network traffic and figure out it did not work as claimed. They have nothing to gain by secretly transmitting data, and everything to lose.
State adversaries are a different story. I don't doubt the NSA might somehow break into Snowden's Echo, but most people don't have such adversaries.
I think it would be entirely possible within US legal framework for Echo/Home to be able to selectively switch from "wake word" to "always listening" mode, on the whim of Amazon/Google or a request of the government. Now, if the government isn't stupid about it and would use it selectively, then good luck tracking it down.
You know what I would want my phone to be doing? To be actually always listening. So that I could just say "Ok Google" at random and interact with Google Now without having to unlock the phone or have it constantly hooked up to a charger. That very simple thing would probably quadruple the usefulness of the whole thing. But Google probably has some "smart" reason for never ever allowing that. sigh
(I mean, what the hell - deep in the options of Google Now I can actually allow the phone to be unlocked by my voice - but if and only if it is plugged to a charger. They had to explicitly code in a special condition to make Google Now less useful.)
(and yes, I know you meant other kind of "always listening")
FYI, some phones actually have this (the Nexus 6 for example). IIRC, not all phones are always listening because of battery concerns, but some phones have chips specifically for listening to "hot words"
State adversaries are a different story. I don't doubt the NSA might somehow break into Snowden's Echo, but most people don't have such adversaries.