For the record, it's interesting to note that, while many FPGA dev boards include the FT2232H chip (because it can be used as a JTAG interface very easily), most of them only route the second channel as a UART interface, while routing a few more IOs would allow the async (or better yet, the sync) parallel mode. Of course, you can always quickly add this kind of interface using a FT2232H breakout board and connecting it to your FPGA board (keep connections short for parallel modes.)
I wonder if they don't wire it up for the parallel mode because that requires host driver support, as it needs to conform to some Vendor-Specific class and not a standard Class? That means host software, too.
For most such boards I've seen, the FTDI chip still had the original FTDI VID and PID (and not a custom one) and thus the required driver is already there on the mainstream OSs without anything extra to install. Without such drivers, the JTAG interface would not work either anyway, there's nothing "standard" about it. You NEED FTDI drivers to make them work in JTAG, at least on Windows.
So, I dunno. It's just probably because the designers either want to save IOs for their customers, or because they don't even know about the parallel interface of those FTDI chips and merely all re-use common application notes/schematics from their competitors, and they all do the exact same. Laziness.
But as we mentioned, Numato has done this, and it's handy. Otherwise, as I said, it's not hard to use an extra breakout board for a FT232H for instance and some wiring, but embedding a FT2232H on board and not being able to use it "fully" is just waste IMHO.