Ultimately, the service enables people to order from Amazon and gathers training data for their algorithms, so regardless of whether you're using it through an Echo or a Furby or whatever else, they win.

To put it bluntly, why would they stop others from making their profitable data collection easier and doing it for them?

https://en.wikipedia.org/wiki/Amazon_Echo#Privacy_concerns

I'd not be that surprised, if when you build with it it has the same kind of features as an echo. Wanting to play music means you are more likely to get amazon music prime, or pay for song storage. Ordering directly and making shopping lists pushes you towards amazon.

It may be cheaper for them than the affiliate scheme.

Amazon want to have their voice-recording and person tracking capabilities in as many places as possible, tracking as many people as possible.

If you want to build hardware for them, convince users to install it, and send all the juicy data back to Amazon, why would they try to stop you?