Why doesn't PCIe and similar signaling systems use full-duplex links?

I think you are assuming here that the number of physical lanes is the bottleneck, and that if you only had more bandwidth then the logic inside the GPU would no longer be held back. I don't think that is really the case. To give you more bandwidth in one direction you need more area, power and resources dedicated to say receivers. Then your whole pipeline has to be designed to support this new double dataspeed. Not to mention a high speed serdes is a complex beast, so now you'd be making each piece even harder by trying to support both RX and TX.

When designers want to double bandwidth it's simple to just add lanes, just step and repeat. When PCI-SIG wants to increase the max speed for the next generation it's easier to just add features and increase frequency.

PCIe in particular is based on the concept of each lane pair being bi-directional. From the time it starts up and negotiates speed and TX/RX parameters, to later on for flow control. If you decided to take away one TX and change it to an RX, now another TX in a separate part of the chip would have to take over it's duties and it all gets pretty messy pretty fast.

Technically though if someone wanted to design a HS link system that allowed you to change your TX to RX for extra receive bandwidth it could be done. But it really would only make sense if pins were expensive because why add all the complexity to your system and design to support this when you could just add a few pins.