While it's true that there a wide number of applications, and Aluminum is theoretically perpetually recyclable, there is still a small problem. When an alloy is formed and elements added to pure Al they are exceptionally difficult to remove. This means that for alloy-specific applications the recycled 'aluminum' must have extra elements added to create the alloy desired.

With continued recycling [over a long period of time] there is concern that alloys will converge upon a final aluminum alloy and we will no longer be able to create new application specific alloys.