There is no sine wave generation here;
Yeah, there is. Well, more often a dirty trapezoidal approximation. I just don't think you've realised it's there. Just as the PWM burried inside an old ARB from the days before fast DACs can produce a sine wave when filtered, so does the PWM from motor controller when filtered through the resistance and inductance of the motor windings. (Some motors have windings distributed in such a way that at trapezoid is the right way to drive them, some want a pukka sinewave.)
These show phase to ground voltages on the output of an RC model's ESC. Remember this is a three phase Y motor so to get phase-to-phase voltages or phase-to-Y you have to do some arithmetic on the waveforms shown to get there.
Look at the envelope - a messy trapezoid.
Similar sort of thing:
Oh, good lord, here we go again; same old argument as trying to explain to a plank pilot why quadcopter ESCs need to be so different from plank ESCs...
That's a waveform from an old eFlite plank ESC; literally more than a decade old in terms of design technology. They operate at about 1/100 the RPMs of a modern quadcopter ESC, and they were DELIBERATELY trying to do MSW the same way as some AC inverters do to get "smoother power" because low-KV motors will shake a wooden craft to bits if they start "cogging" at low RPM. They were able to do this because the demands were so low on the processor. Many of these ESCs actually have a governor feature in them that can be turned on to provide a fixed RPM for helicopter use.
That is literally not even the same species as a multirotor ESC. Yeah, sure, you can see something sortof like that waveform with a multirotor motor & ESC... only far fewer steps in the waveform and a lot more noise because it is literally commutation going on (the ESC people's term, not mine), not any attempt at sine wave generation.
I spent a lot of time at the beginning of my multirotor journey trying to reconcile my conventional knowledge of conventional industrial speed control with how these ESCs work. In the end, I came to realize this was not a case of "derivative" as much as "divergent evolution" from a really old fork in the way back when. The needs of an aircraft that uses varying speeds of motors to fly, steer and keep itself level are completely different from anything that has gone before. As long as you keep trying to fit MR ESCs into any existing boxes, the less sense they'll make.
mnem
The exact model of ESC doesn't matter - I just did an image search and picked the first couple of waveforms that looked right. What matters is that it controlling a BLDC motor.
Mnem, this is about how BLDC/PMSM motors work, no more no less. It has nothing to do with the application. BLDC motors do not blow themselves up if they have no load, etc. etc. It doesn't matter is the BLDC motor is a lift motor on a quadcopter or a servo on a CNC axis, it's still a BLDC motor. I've got two of the quadcopter type external rotor motors here, I've also got two small circa 50W "just a motor" BLDC motors. They are all the same electrically. Three phases, Y wired, a bunch of stator poles, a bunch of permanent magnet poles, that's it all for the 'motor' part. They take the same electrical signals to make them go around in the same way, the physics of magnetism dictate how they work, they all work the same. The torque/speed curves of all of them are the same fundamental shape and so on.
By pure coincidence I've spent some not inconsiderable amount of my time for the last few months reading real text books on the subject, watching loads of videos on the subject, including the whole of a two day TI seminar on the topic. I don't claim to be an expert, but I can claim to know enough to say "Hold on, that doesn't sound right" or "Yeah, that sounds right". Robert clearly knows what he's talking about. A lot of what you've said doesn't make sense. I pitched in to try to give you a face saving way of coming around and you're refusing to take it. So be it, it's your loss.