I'm designing an interesting piece of hardware: a 4-digit 7-segment LED display with shift registers and exact foot print as a 16X2 HD44780 display, even the 5V and GND pins will match, besides the shift register pins are on the HD44780 D5-D7 since most people use 4 bit mode. This will a drop in replacement of a 16X2 HD44780 display. You just have to use the right program to work the shift registers but all pins fit and so on. I ordered some LEDs already. Will start design once the semester is over. This will be great for clock projects.
Yes, a small processor could replace your shift registers and expose a hd44780 interface. It would likely be as cheap if not cheaper, and easier to use fir he masses
I desolded the chip off a broken 16x2 lcd and transplanted it onto my own led matrix board and communicated useing the original lcd interface useing 4bit to make a 8x2 or 1x16 display depending how it was wired.
The HD447800 chip can't drive the leds directly without row driving transistors but the concept is proven
