“... 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.
It’s true that the “refinement” costs are significantly lower for recycling but the “exploration and production” costs for recycling are significantly higher.
So if you could build the plant right next to the aircraft graveyards in Arizona for example, yes then it would be beneficial, but even then you need to wonder, if recycling is so much cheaper, why are there still planes in graveyards?
If you look at the numbers it’s obvious why this is the case. 1kg of newly refined aluminum requires about 75c - $1 in electricity to refine and even with that the total market cost for 1kg is about $1.50.
Those costs are so low that they can be easily clobbered by an inefficient collection mechanism. Just as an example, if I have to drive 10 miles each way to the collection point and I do it every time I collect 1Kg of household aluminum I have blown $2.50 in just gas costs alone! Not to speak of the wasted time in driving, separating/washing and storing that junk.
Recycling anything including aluminum only makes sense if you fool a number of people to subsidize your logistical collections costs.