OK I stand corrected - maybe! It was the way I was taught, 30 years ago. It was still taught 11 years ago when I did my instructor training. Perhaps modern cars have more robust mechanisms, but it would still be good practice for learners to depress the button when applying the handbrake as they are likely to be driving older cars once let loose on their own.Extremely unlikely, it appears manufacturers manuals seem to state button only used when applying handbrake.
Apart from anything else, the noise of the ratchet is annoying IMHO, so I will always use the button.