That was the theory in the past, along with the habit of tossing it into the river to carry off to the sea. But 70 million inhabitants create a lot of garbage and the river can't handle it anymore, not if it is going to provide water for the Delta downstream from Cairo. The problem with taking it out into the desert is the fact that there are no roads out there, other than the roads that are leading to new settlements, and the people in the new settlements don't want garbage there either.
Cairo, with a population of about 20 million, has had a trash problem for millenia and even now we have a group of professional trash recyclers near the city who have made their lives around the collection of garbage and the resale or reuse of usable items. They are known as the Zebaleen, or the garbage people, and the life they lead is not a very pretty one, but the job that they do is essential and well done. They will be seen throughout Cairo and the surrounding areas with their donkey carts picking up the trash to be taken off to their settlements near old Cairo. Cloth will be recycled into rag kilims and paper into recycled paper. Glass finds its way back into the souq where hand-blown vases, glasses,and dishes of lovely shades of blue are sold to visitors.
There are NGO's working with the Zebaleen to help them to market their recycled products, to run schools and hospitals for them to improve the quality of their lives and so on. There are also foreign companies that are hired to collect trash in large trucks that carry the trash out into the desert where it is dumped in pits and left to rot...or to blow away in the first high wind. On the whole, I believe that the efforts of the Zebaleen are the more effective. We have the Giza dump just over a hill in front of my home. Years ago it was much further away, but over time it is creeping closer and there are days when the ripe odor of rotting garbage wafts over the desert where we love to ride. Not nice at all.
My neighbours have to pay to take trash to the dump and being farmers with very little disposable income, this is a problem. They try to burn most of their trash, but some of it ends up in the canals. The wealthier inhabitants of my neighbourhood pay for monthly trash collection in which our households subsidise collection for our less wealthy neighbours, but the Giza dump is not my idea of a solution to the problem. The farming areas where there are no shops to distribute plastic bags and packaging are noticeably cleaner than the areas closer to access to the "modern conveniences" like a styrofoam tray for your cheese. I drive the grocery store clerks nuts when I suggest that I don't really need one.
One of the newer trends that I've noticed is that some of the farm families have started their own recycling plants where they collect plastic materials for sale to other companies. Not very pretty or picturesque, but it's getting the job done as well. Sometimes the most effective solutions aren't so pleasing to the eye.