I don't know where singers learn microphone technique. Most singers in popular music don't have any training, so they can only have picked it up from seeing other people do it, or in response to what they hear coming through the speakers at their live gigs.
The 'classic' microphone technique is to back away from the mic when singing loud, coming in closer when singing quietly.
This does work in live performance, particularly in smaller venues where the sound is often less well-controlled than at top pro gigs.
The alternative is for loud sections to be either ear-splitting or distorted, or for quiet sections to be inaudible to the audience.
Of course a compressor can be used, but this creates other problems in live performance that we won't go into here.
In the studio however, things are a little different.
Firstly, there is no problem in setting exactly the right preamp gain to capture the loudest sections of the vocal without distortion. There is never any reason to back away from the mic due to excessive level. (And if the mic can't take it, switch in the pad or use one that can.)
Now if the quiet sections of the vocal are too quiet, they can be brought up in level using fader automation. You will probably be using a compressor that will do some of this work anyway.
So there is no reason why the singer has to be anything other than a constant distance from the mic.
And in fact, if the singer does bob backwards and forwards, it creates a problem. When you use a microphone close up, the sound quality it produces changes significantly even with slight changes in distance. This is particularly so with directional mics, which exhibit the proximity effect where bass rises when the sound source is close to the mic.
Randomly variable level, bass and sound quality is most definitely an engineer's nightmare. It could take a day to put right, and even then not perfectly.
So in general, it is better in the studio for the singer to stay at a constant distance from the mic.
There is however an exception…
Sometimes it is desirable to let the singer react to what they hear in the headphones. Some experienced singers have the ability to 'work' the mic to get a more expressive performance.
In this case, you should make sure the singer has exactly the headphone sound they want, with EQ, compression and reverb as required. Then let them use their microphone technique as they wish.