When Amazon Music Unlimited was an attempted thing, that was a direct path to monetization that basically only happens if you have Alexa/Echo widely deployed. Otherwise, it seems a tenuous link to increasing sales in retail.

(I say "was" because they recently rolled part of it out as a Prime benefit a couple of weeks ago, but I can't figure out the exact difference between unlimited and what's included in Prime [and don't care enough to chase it down], but they are still offering a $9/mo unlimited offering, so there must be some difference.)