I wonder why there isn't a $20 PCI-E card (or perhaps USB dongle) that offers a 40-pin RasPi-style port.

I don't know about the prices but mixed-signal GPIO rigs for PCIe and USB are very common. Look at the "LabJack" for example. The LabJack U3-HV has almost exact feature parity with the geekport.

A quick google puts it at $130, well beyond the price of "just buy a Raspberry Pi or similar device, which also comes with all the SoC smarts too."

Fair enough. It compares more favorably to an odd port inconveniently located on the back of a $5000 (2022 dollars) tower PC.

If you had a PCI card you would need some kind of external adapter or breakout box for the GPIO pins. Seems much more practical to have the board in the "breakout box" and connect it via USB.

Twenty years ago I might have liked that too, but these days I much prefer dedicated machines (MCUs like Arduino, P8X32A, R.Pico etc. or "single-board" (or rather "open-frame") computers like R.Pi, BBB etc.) for the acoustic noise alone (not to speak of power bill and electrical safety). USB or Ethernet (preferred for galvanic separation) on the PC does just fine to connect to those.