This is an interesting discussion & it never ceases to amaze me, after
a long time away from news groups, how passionate people can get about
a simple question to which there is no one right answer.

I'm a fan of the parchment paper approach, simply because I find it
easier than struggling with a pizza that has adsorbed to my cheap
wooden peel (no matter how much cornmeal is applied) after someone has
distracted me during the construction process. Certainly the moisture
content of your dough is a factor here, as is the peel material, as is
the amount of time the dough sits on the peel, cornmeal etc. A
nonporous (metal) peel would contribute to letting the dough slide onto
the stone. You would probably still need some kind of granular skid
(the cornmeal) & the faster you move the more likely you will succeed
in getting the pizza to slide cleanly onto the stone. My kids
complain bitterly about cornmeal on their crusts, so the parchment
paper is another plus there.

I do agree that if you can avoid the parchment paper you will likely
have a crisper crust as you will get more water removed from the crust
during the baking process.

I have never used (or heard of) a pizza screen.

My conclusion would be that it is a matter of personal choice as well
as what works best under your own kitchen conditions, with your
equipment etc.

PS I would agree that 400 is not hot enough. I preheat to 450 and bake
for 10 minutes & the result makes my family happy. Plus it gives me
time to make the salad and wash the bread machine pan.