Would they? Aluminum needs a lot of energy to melt and then reform into something new. Since the alloy is not known they need to refine the different metals out just to ensure that they get the correct alloy for the user. Mining Al uses a lot more energy.
That is I suspect the total damage from new plastic is less than recycled Al. Someone needs to find numbers to verify this of course.
I'm finding info of just 5% from a scrap ingot:
https://aluminium-guide.com/aluminium-alloys-food-beverage-c...
I've wondered about this because I've heard the same thing from my partner - in Engineering school in Spain, she was told that waste aluminium as a building material should be avoided because it was so expensive to recycle. But we recycle aluminium here in New Zealand - perhaps it's something to do with being able to use green energy at night (New Zealand has abundant hydro power)?