I have heard of this, but it is now again coming from the “classical” guys. I switch among my 7 guitars with 12, 13 and 14 fret neck joins and varying scale lengths. Sometimes, after a long trip with just 1 guitar I will notice a slight adjustment during warmup, then I am good to go.
If you really want to appease the instructor you could store one for a while, then it will be an awesome rediscovering of that guitar when you get back to it. I am no professional, but I don’t think you should give up a beautiful guitar on this advice alone, you will regret it someday. As you want to try different styles, you can do them all on one, but you will find certain guitars lend themselves to certain sounds, why limit yourself.
Good luck whichever way you go.