If nothing else, it can ruin the flavor and texture of foods. Foods stored in aluminum long-term take on a "metallic" taste.
PErhaps this also means the food contains dangerous levels of aluminum. Or maybe it just means that you're expensive, carefully prepared whole foods now taste awful and are wasted. In any case, it's not a good choice.
Wax paper or parchment paper is a much safer option- you can wrap foods in paper and then a layer of plastic wrap or aluminum foil. Or, you can just use the plastic. It probably does leach a little bit, but it won't ruin the flavor of foods. Glass or ceramic are by far the safest choices for food storage.
PErsonally, I use glass as much as possible, but I do keep plastic baggies on hand in case I'm out of clean jars, or don't have one the right size (and the bigger one won't fit in my stuffed fridge.)