A.M. and F.M.
As to the long-standing AM vs FM debate, Barry and I have the distinct advantage of a close liaison with a radio consulting engineer who does understand the math, and he has provided us with copies of the earlier Carson papers. When we get into discussion about this, his read is that one is a half-full cup while the other is a half-empty cup. In other words, when you optimize each, they are so close, it's hard to find a difference.
Let me give you an example I can explain: When I was a product manager for modems at Paradyne Corporation, we were pushing the limit of commercial viablity for voiceband modems. Our designers chose phase-modulated modems, while our arch-rivals, Codex, chose what was the university-professor; math-on-the-blackboard textbook favorite, vestigial sideband AM modems (which is what the Bell Labs engineers were big on, too).
I had to come up with some advertising for our salesmen to sell with. So, I asked our designer what it was about. Tom Armstrong (that was really his name!) told me, "VSB has a textbook advantage of 1/2 dB in signal-to-noise requirement over PM. But, none of its proponents took the time to find out how long it takes a VSB modem to regain sync and get into operation when there is a noise hit. That is so much longer that, over time, a PM modem gets much more data through. We think that data throughput is what our customers want, not theoretical perfection."
Hey, I just paraphrased Tom's words, and we devastated the competition! And, addressing some of your remarks, yes, early FM was quite complex compared to AM and SSB, which would be less expensive to manufacture. But, there's a key point in the AM vs.FM story that gets lost: The others really wanted Armstrong's FM but they didn't want to pay him patent license fees. (I dearly wish I hadn't let the Armstrong patent license document that hung on the wall at WTSP-FM next to the FCC license get lost!) Armstrong's patent was limited. He defined FM as a high-fidelity radio transmission method, and said it required a modulation index exceeding 1.0 to get the 60 dB S/N that made it "hi-fi." Bell Labs dearly needed FM to make its microwave systems work. They limited their modulation index to less than 1.0, and invented "phase modulation" for the world -- and themselves to be patent license free! Sarnoff went a bit futher. He waited for Armstong to commit suicide, then let RCA loose on FM for both TV audio and radio broadcasting. So, you see, usable systems can be made of both AM, FM and even "substandard" PM, if you just optimize the system they work in.
I am constantly amazed at how few people understand the concept of a "noise floor," and how, because we badger authorities like the FCC to allow more and more stations, we have raised the noise floor. Just a week ago, I happened to be at a convention of broadcasters in Charlotte, where two were amazing themselves about how a new AM station on the California coast, operating in the new expanded AM band above 1600 kHz, said they had listeners in Hawaii. Well, duh - first off, 5,000 micromho saltwater for a path, and then nobody else on the channel to create interference! What do you expect? And, how long before there is someone else on their channel, anyway?