I don't believe it does, otherwise there would be companies willing to pay you for your scrap aluminum.
The only thing that "makes sense" is for the government to force millions of people to waste time (labor) sorting the aluminum, then take some of my money and give it to companies willing to haul it, then give the scrap away to companies willing to recycle it, after giving them tax breaks and incentives using yet more of my money.
In that sense... it make sense :-)
“... otherwise there would be companies willing to pay you for your scrap aluminum”
There are and they do.
It is many times more costly to produce aluminum from ore than to melt down existing aluminum. It is a deeply electricity-intensive process. Essentially, it takes a medium sized power plant to refine bauxite ore to aluminum.
It is the only clear example of where recycling does make sense.