Regarding pitch on the structure:

I agree there should be some pitch to the roof. The former roof, with no pitch, would randomly douse you with water after a rain.

But the taller the shade structure’s eaves, the less shade you have when the sun is at low angles.  It’s a tradeoff between headroom for tall people and shade.

If the high side is to the east, there will be less shade in the morning, and the roof will have a positive angle of attack for Santa Ana winds.

I think a gable roof or a hip roof would be better.  I particularly like the hip roof, because it slopes down in all directions.