I teach a lot of pirouettes from 5th position because, as my theory goes (and you’re welcome to weigh in), a pirouette is a balance that turns. Therefore, you must find that balance over the supporting leg first. At an advanced level, students might be executing turns from grand pile in 1st, 2nd, 4th, and 5th. But I feel the 5th position is an excellent place to feel the elevation of the body (they would prefer to ‘spin’) which informs all the other turns.
I will give consecutive pirouettes from 5th, putting the foot back down retire or keeping it up in passé for fouette preparation. It works well to give students an option as many of my classes will have students of mixed abilities. So the stronger ones can do double, single, and the weaker ones might be doing 16 consecutive passé retire releve (or 15 retire, 1 passé change).
I have been known to do brutal adage that includes the grand plie to pirouette from all positions that opens to a la second, arabesque, or developpe devant for my most advanced students. That one is an ancient Russian exercise that I give occasionally but it too is fraught with a variety of ways students can ‘cheat’ (so of course they try). But I think it’s grounding mentally and physically. The pirouette from 2nd is good for my contemporary dancers who tend to lower their heel in the middle of a turn (sloppy technique) which over time becomes a stubborn habit that’s difficult to break.