There really hasn't been any point to recycling paper, plastic, and glass for quite some time now. Recycling glass hasn't made sense ever since local bottling plants ceased to exist in most cities, removing the system by which they were able to re-use recycled bottles. Recycling paper is obviously no longer a sensible activity given the issues of contamination and lack of economic incentives given just how cheap sustainably harvested wood has become. Plastic, well plastic would make sense if we could ever figure out how to sort all the different types automatically. The re-use of recycled plastic is basically limited to a handful of common product types (plastic bottles that are either HDPE or PET and easily identifiable as such).

That said, one should always make an effort to recycle aluminum properly. There's a reason aluminum is often referred to as "solidified electricity" and it's because it takes enormous amounts of energy to extract aluminum from raw ore. Recycling finished aluminum goods cuts out that entire step of the production chain and has an enormous impact on large-scale energy consumption.