I know a lot of people that do this... a couple of thoughts..
I stretch them. I stretch each string as I change them (I change them one at a time).
there's really no need to do this 'one by one' approach
it's slower and you have little to gain from it..
I've never seen a luthier do this..
and you will not be able to polish the frets...
polishing the frets is important so that the contact points are nice and clean
and polished frets also feel a great deal better when you are playing..
try using a cotton bud to wipe a little polish over each fret [being careful to not get any on the fingerboard]
then polish off with a soft, dry cloth
it's just enough to take off the layer of oxide and guck that builds up on the fret crown..
it really makes a difference
just ensure that when you remove the strings that you wind off all the tension before cutting them
or if you have a whammie, dive-bomb them slack and then cut them..
all you need to avoid is the sudden release of tension.. most likely won't do any harm, but certainly won't do any good..