If we assume 2 gold = 1 cog, then it's the same yield of a regular worked tile in the middle age - mined hills are already better. And it's important to consider that in order to build petra, the city needs to already have decent production. You can't just settle in the middle of the desert and hope petra will make it all right, unless you are quin shi huang. So when you complete petra you will already have good tiles to work in that city. you could work that desert if your city keeps on growing, but given housing limitations in early ages, it's unlikely you will grow it much more. Until the modern era, when the tech bonuses to various improvements will make the base desert yields very bad compared to other tiles. So a city on flat desert with petra will always be no better than a city with normal terrain, and it will be worse in later eras.
there is also the opportunity cost to consider: you must settle a city near desert, try to build a wonder, if you lose the wonder the city won't be able to grow, if you get the wonder it's still no better than having settled on any other place. So I settle first on good land, and by the time I think "the only place left to settle is desert, may as well take it and try petra" petra will have been taken already.
At least that's my experience about it.
I concede you the point about unique improvements, though. In general, petra is good if you can get something in addition to that 2-1-2