Ahh, now were getting to the good part...
Making what was symmetrical, and linear, - now asymmetrical and non-linear...Swing or not, - non-linear amplification is what many would call "swing".
FM is a type of "Swing" - on better defined as "deviation"
AM, carrier - being "Steady" - is a requirement for the "modulation of the envelope".- but not really for sending, only for receiving (Detection) - else SSB would not even exist.
So when deviation is not excessive, or non-linear - you have symmetry.
Same can be applied to the equal halves of a AM envelope - even fully modulated, still averages out to be Carrier + Audio Power in it's sidebands. But only when it's modulated - in other words, action has to take place to form the envelope - so modulation is that action to generate it. So when no audio is applied, you have just carrier.
Yes, you can get carrier and audio to be just as steady due to symmetry. It's a part of what Class D is, you are borrowing from carrier to provide envelope.
The FM side of things is similar, only you waste more BANDWIDTH using greater levels of Deviation than carrier to envelope.