This is a bit of a naive analysis. Amazon's margins aren't "razor thin". They're thin in some places but huge in others. AWS, for example, has a 50% gross profit margin, and their gross margins on digital goods (mp3s, ebooks) are also high. These aren't small potatoes, these are multi-billion dollar businesses in their own right.

As for shipping, amazon already has a delivery service (amazon fresh) but I don't think they have a strong desire to completely own delivery, they have very cozy relationships with all of the major shipping companies. If you knew how much money amazon actually pays for shipping you'd be astounded, they're very good at using their volume as negotiating leverage.

Logistics is at the core of amazon's business though, and it's a big reason why they are succeeding where others are not. If you order through amazon you can expect most items to be en route in less than 24 hours. That takes a lot of work especially considering the sheer quantity of stuff they offer.

Aside from that, they aren't just trying to do one thing, they are trying to diversify the company, so that it will rest on multiple multi-billion dollar divisions over the next decade (retail, AWS et al, ebooks, mp3/VOD, etc.)