Excellent way of describing the difference of the systems. I would also add the ability of accurate focus across nearly all the sensor area. With the Sony A9 for example, 693 phase-detection autofocus points offering 93% frame coverage. The ability to hit nearly any part of the frame and keep it in focus is amazing technology.AFMA can be a pain, but once done for a particular body/lens combo it works fairly well without needing to be redone very much, particularly for primes.
The real advantage of main sensor based AF over dedicated AF sensor based PDAF is that it's right at all subject distances if the camera optically confirms AF rather than only confirming the lens moved the instructed amount (which is what the most advanced PDAF systems do when shooting fast bursts). By the time the lens has moved, the mirror is already swinging up again and the lens position is measured by position sensors rather than optically. But some DSLMs also do not wait to optically confirm AF before resetting the shutter curtains to take the next frame in a fast burst. That's why some DSLMs also have forms of micro adjustment - to calibrate the lens' AF position sensor(s).
You can't use a DSLR in Live View with your eye to a viewfinder.
You can use a DSLM with your eye to an EVF.
There's still a fundamental difference there. Sometimes camera stability is critical in an environment where using a tripod is not practical or even possible.
Maybe there is someone somewhere that does it that way, but I know of no pro or even advanced amateur who uses a rear LCD screen to shoot sports/action stills.