The console makers require that developers sign an NDA before gaining access to their API.

Why?

Why don't you ask them?

If I were to guess, I'd say it's to prevent both piracy as well as games being sold from 3rd party markets.

To make sure no one can make games for their platforms without their permission and agreeing to their terms. If the platform was open, anyone could make anything and sell it in any way they wanted - so how would they squeeze more money out of them for themselves?

If you look at the history of consoles, many are sold at very thin margins, or even at a loss, not even including R&D, distribution, etc. just purely from a component cost standpoint. They recoup these costs using revenue from the game sales and the online play features. It’s not a squeezing money kind of thing. For example, the next gen of consoles is probably going to be in the $500 range, and includes pcie4 speed 1tb SSDs. I bought one of these for my new machine and it was about $200 alone. Add in the processor, ram, motherboard, case, optical drive, etc. and these systems are not making tons of profit.

Presumably the console manufacturers would not allow this. They want more control than that and don't want licensees acting as a sort of sub-licensor and building things for people like this.

You have to sign agreements with the console manufacturers - they get to set any rules the market will support.