I've seen it a couple of times. Late last winter they had a big sale; many buttons were $.99, and some were $1.99, though they still had a limit to the total number you could buy. (Wait... maybe I'm wrong about that. I bought ~20)
I'm guessing that as it became clear to Amazon how many buttons were selling without ever having products associated, they caught on. Their 2nd gen IoT button costs $19.95!
It's true that Dash buttons are little advertisements, but that not the only way Amazon sells or promotes them. Two examples:
You can buy a Dash button unsubsidized as the AWS IoT Button. However, you have to do the coding (as some on hackster.io have done).
An Amazon Button partner can build on top of Dash as Visybl is doing with their goButton. The only downsides here are that they are still in the KickStarter phase and, last I saw, they were focused on business use with sales of 50 or more at a time.
So, no, I don't think it's out of the realm of possibility to find a similarly powerful option without me having to create it myself.