"Um, why would Netflix agree to ongoing, recurring payments for a peering agreement when they could have simply have incurred a one-time cost by adding some hardware on their side? I believe it is because the missing resources were not on Netflix's side of the connection."
It's traditionally the way the Internet has worked, for better or worse. Peering was between "peers", ie other ISPs with some expectation of mutual benefit and equality. Naturally this begat peering wars, Tier-1 bragging and the Net Neutrality debate. If you're not a peer, you pay something towards the cost of delivering your bits. Netflix doesn't want to pay if it can help it because obviously that becomes an operating cost that eats into it's margins and profits. Situation gets a bit more complex when ISPs like Level 3 and Cogent are involved. But basically it's an issue with the way the money flows, and pretty much a plain cost to your ISP.
User > Netflix
Netflix -> Cogent/L3 <-ISP <-User
So double dipping is really from Netflix's transit providers, as unless the agree to free peering with the ISPs connected to them, the ISPs would also have to buy more transit from Cogent/L3.
"And again, um, isn't that how the Internet works? Users pay for a connection, then go out to external sites and exchange packets. Yes, when the packets consist of a video stream from Netflix the arrangement is pretty one-sided, but then this is >>EXACTLY<< what ISP's expect. My connection is rated for 50 Mb downstream, but only 5Mb up..."
Yes, to an extent. Unless you're a business user or running servers at home, usage patterns have pretty much always been asymmetric since the good'ol days of 1200/75 modems. Difference is the amount of traffic generated by traditional usage, ie email, web, VoIP, gaming and streaming large amounts of HD video content to millions of users. That's not something the Internet was ever really designed to do and just highlighted settlement problems. Which isn't something new and the voice world solved it over 100yrs ago. If originating/terminating traffic balances, costs net out, otherwise one side pays the other to reflect the costs of delivering the other parties traffic.
"Why does a packet from Netflix "cost more" to deliver to me than a packet due to downloading an ISO image from Debian?"
Assuming you're downloading from the same place, it wouldn't. Difference is you're probably not downloading those images every night. Just like I'm not downloading 11GB from Steam every day. Plus if there's congestion, your download can be slowed down and it'll just take a little while longer to complete. If it's video, the ISP probably has no control over the session and if there's congestion, playback stops and user blames their ISP. Or Netflix blames your ISP. Or your ISP blames their transit provider for not increasing capacity. Widespread video streaming massively increases capacity needed during peak busy hours, and if content providers won't contribute towards those costs, the only option is again to charge the user.