> just as we don't re-prove Fermat's little theorem every time I use it in a proof
Exactly! There's a shared foundation, and everyone builds upon it. A mathematical paper is a whole bunch of Lego blocks being added to that foundation, and combining them in a hopefully-useful new interface.
But if the entire paper is just one giant black box, you only get to use the final interface: you lose the ability to meaningfully repurpose the individual Lego blocks to build a different interface. You end up having to reinvent the same Lego blocks over and over again, just with a slightly different color each time.
Don't want to re-prove each and every Lego brick? Then you shouldn't accept giant black box proofs.
Exactly! There's a shared foundation, and everyone builds upon it. A mathematical paper is a whole bunch of Lego blocks being added to that foundation, and combining them in a hopefully-useful new interface.
But if the entire paper is just one giant black box, you only get to use the final interface: you lose the ability to meaningfully repurpose the individual Lego blocks to build a different interface. You end up having to reinvent the same Lego blocks over and over again, just with a slightly different color each time.
Don't want to re-prove each and every Lego brick? Then you shouldn't accept giant black box proofs.