Key Management: Why would use of publicly-available electronic documents as one-time pads not provide essentially unbreakable encryption?

Well, you would have to use it to seed a cryptographically secure pseudorandom number generator, because there's a lot of structure in the bits of NYT obituaries. If you do, your message will be as secure as the weakest of these links: 1. Someone breaking (or having a backdoor in) the prng 2. Someone guessing your shared secret. This is not as hard as you might hope. If you asked 100 people for a suggestion of where to go for "random" data,  odds are good one would suggest exactly the same as you (New York Times obituaries, White House press releases, etc.) You also have the problem of agreeing on where to get your key data, which you have to do over a secure channel.

Part of the security of the OTP is that the you take the plain text and xor it with a random key.  NYT Obit's nor quora posts are random.  While this sounds simple in practice is seems very problematic.  Similar operational problems have compromised crypto systems.  So you would need to: Agree on a URL and likely a time stamp in case it's changed.  Pages like the NYT and quora posts often get edited and even a single bit can make a difference Some how coordinate who is going to consume those bits.  Is Alice always sending to Bob?  What if Bob wants to send to Alice? What if Alice wants to send more info than the agreed on post? What if attackers correlate the web traffic of these two users and notice that Alice hits a URL, sends a encrypted message, than bob hits that same URL? So kind of fun to think about, but generally I'd recommend AES256 if you can agree on a key in person, or strong public key crypto (3072-4096 bit for RSA, 521 bit for ECC).  Of course that still gives the attacker potential information on who you are talking to, how often, how large the messages are, etc.A better use of websites that allow posting is to hide information in those posts by some agreed upon method (search wikipedia on strenography) so an attacker would have a difficult time telling not only what you are saying, but to whom.

It would work ok but, it would be vulnerable to many other attacks. mainly, attacks against your computer itself to find unencrypted info about what your using for a key. Also, since the only secure way to share what 'pad' is to be used is a face to face anyway. why not just have a pad generated and exchange it. Back you your idea, you could even change the pad to a new location and send it's next location as part of the current message. True, unbreakable messaging would need a hardware random key generator on a standalone(no network) box. Something like an overdriven microphone recording an Air Conditioner unit, a Lavarand setup, or something else to generate large amounts of truly random data. Then chop that data up into tiny, sequential sections, burn a copy to a DVD, blueray, big USB drive(depending on your size needs) to hand off to the recipient. Then use something like Hardencrypt to encrypt your message with as many sequential blocks are necessary to cover the size of your message, on the totally offline box and burn your encrypted message out to CD to send over the net. Then shred your CD. Then the recipient reverses this process, burn to cd, stick on their stand alone box, and decode, shred. This protects online interception completely. Physical access, could be protected somewhat by running Truecrypt on the standalone but, short of Thermite, physical access is game over. Also, once one side is compromised, non-repudiation becomes an issue.