> Covering a skylight with solar is a net energy win, as would taking down the tree(s).Solar isn't the only thing people are optimizing for -- skylights and trees are pleasant. The trees also aren't on our property, and even if you removed all the parts over our property our east-facing roof area would still be completely shaded.
> Trees are also going to block the front of your building even more than the southern facing roof.
It depends on the situation. Our roof is East-West with a big Gable dormer halfway along the West side. The East side is fully shaded by a tree, as is the back of the West side, but the front of the West side and the South facing side of the dormer get good sun (and now have solar). Our house faces the street, and there aren't trees in front of our house, so front-facing solar would work well if that was a thing people did.
> Getting shade from other buildings on your roof is also unusual for 2 story buildings.
I agree it's unusual in general, but houses here are close enough together that some roof shading is the most common situation.