"by increasing the frequency of orders via Amazon, it gives them more power to negotiate better shipping rates, negotiate better bulk rates on products, and expand their distribution network"

I'm skeptical that that is happening (Prime doesn't represent a giant change in volume for them). But let's assume it is, then the benefits should affect all their customers? So non Prime users end up being overcharged?

"Also, Amazon loses a hell of a lot on Prime directly, though I'm sure they just view it as subsidizing growth. I'm sure they've lost money on my shipping, at least."

Maybe you have managed to "beat-the-system", just like people that cycle credit cards end up making off with more money than they give the CC companies - but on average people are being ripped off.

There is no growth to subsidize b/c that only makes sense if they had a mechanism to cash in. If they drop the free shipping then people will stop paying for Prime and will switch to other retailers. Slowly raising the prices to a point where you stop loosing money and then hoping people keep shopping at your website b.c of habit is also a short term strategy.

On a side note, leveraging their size to get preferable shipping rates is also anticompetitive. They aren't a monopoly per se, but they've dominated the market to such an extent that UPS probably can't say no to whatever rates Amazon demands.