Both USB and PCI introduces latencies. These latencies means that bit-banging does not work well. You can't react instantly to control signal change. Extra latencies means that a FIFO is needed.

But the big reason for really huge FIFOs on the USB-connected serial ports is that they not only have a high latency from USB and PCI. They normally also supports baudrates of 1Mbit/s or more - the 16-entry FIFO is much used and appreciated already at 115200 baud. Step up the baudrate a factor 10 and it is also reasonable to have ten times larger FIFO to allow caching for the same number of milliseconds. At 1Mbit/s you get 100k characters/second or 100 characters/ms. 1ms is also the framing speed of the USB protocol so a FIFO must be able to span (at the very least) this time frame.