(NASDAQ:AMZN) is giving away over 1 million MP3s to every Prime subscriber.

The company unveiled its Prime Music service on Thursday. The on-demand streaming service is severely limited in its early stages, offering just 5% of the catalog of other streaming services like Spotify or Apple's (NASDAQ:AAPL) Beats Music. Additionally, Prime Music doesn't offer an Internet radio feature like Pandora Media (NYSE:P).

At first blush, these obvious weaknesses may make it seem like Prime Music is doomed to fail. But what seem like Prime Music's biggest weaknesses may turn out to be its biggest strengths.

When 1 million is a small number
Amazon boasts over 1 million songs available for free streaming on Prime Music. While 1 million songs sounds like a lot (I certainly have listened to far fewer in my life), it pales in comparison to the competition.

Beats Music, Spotify, Rdio, and Rhapsody each sport around 20 million songs available for streaming. Pandora offers a similarly large set of songs from all the major recording labels.

Amazon's first stumbling block came with Universal Music Group. Although the company says it's in active discussions with Universal, the omission from the catalog at launch is painstakingly noticeable.

Additionally, the service omits songs released within the last six months. This might not be as big of a problem for a streaming service as omitting an entire label's catalog from the library, but it's something all of the competitors have.

Why a limited library may be an asset for Amazon
Amazon operates the second largest digital music store after Apple's iTunes.

The nascent digital download industry is already being disrupted by streaming services. Last year, digital download sales fell for the first time in history. In the first quarter of 2014, digital music sales declined 13.3%, according to Nielsen SoundScan.

Meanwhile, streaming services continue to grow. Pandora, for example, grew listener hours 28% and 30% in April and May, respectively. (Note: That comes after lifting monthly listener hour restrictions.) Overall, on-demand streaming plays climbed 34.7% in the first quarter of 2014.

Apple has responded to the rise of music streaming by joining it. Last year, the company launched iTunes Radio, and the company acquired Beats Electronics and its music streaming service last month. Apple hopes these efforts will mitigate the effect of declining digital sales.

Amazon's billion-dollar digital music store is similarly under attack, and Prime Music is its answer to the plethora of music streaming options.

Prime Music is integrated with the rest of Amazon's music store, now simply dubbed Amazon Music. To play songs, Prime members are asked to add interesting albums and playlists to their personal library, where the free Prime Music is collected along with personal uploads to Amazon Cloud Player and past purchases from Amazon MP3. It puts all of the user's available music in one place.

More important, this seamless integration with the digital music store may ultimately lead to users exploring outside of the Prime Music catalog in order to bolster their libraries. Amazon uses its recommendation engine to funnel users toward actual purchases as well as other free Prime Music offers.

Can the loss-leader strategy work?
If someone is looking for a stand-alone on-demand streaming service, Prime Music is probably at the bottom of the list... unless they've already subscribed to Amazon Prime. At that point, it requires serious consideration, and at least a test run.

That may be one of the keys to Amazon's strategy: Get people in the door with 1 million free songs, then make money on the back end selling them new (or otherwise unavailable) music in the digital download store.

Big-box retailers have used the loss-leader strategy successfully for years. Amazon's entire Prime service is practically based on it. Prime Music is just another extension of the strategy, and a smart one at that.