"But then it evaporates.
Peat moss adds no nutrients. And simply laying it on top of the soil
does
nothing for it's structure. "


Well Duh! Of course water evaporates.. But by the time it's getting
dry, the sprinklers should be coming on to water it again. With the
peat moss or another appropriate top dressing, you can go a lot longer
between waterings. And it's not there for nutrients or to add
structure to the soil. It's there to keep the seed partially covered
and damp while it germinates. Ever see hydraulic mulch that's used
very effectively in commercial hydroseeding? It does exactly the same
thing.