The floppy port can provide more power than the parallel port but I don't think it would be enough to run a Raspberry Pi, certainly not a V3.
Well, I certainly would not expect to power it through the port. The parallel port also does not have enough power.
I suspect the max transfer speed of a parallel port would be faster than the floppy port. Also, DE-23 connectors are hard to come by 
Fair points, but from experience, the parallel port sucks CPU power, whereas what happens on the floppy port can use DMA.
There's a similar project for the Apple ][ called Apple2Pi: http://schmenk.is-a-geek.com/wordpress/?p=167. It uses a serial link to communicate between the Apple and a Pi at 115Kbps.
Right. On Amiga, do not expect more than 57600 baud on the native serial port if you want it to work reliably, on many systems you may even have to drop lower, and CPU will be plenty busy too. Just about anything is better than using the serial port.
I think it would be much easier to build the higher level parts of this using a normal slow null model cable between the Amiga and Pi. The fast low level Parallel to GPIO protocol could be plugged in later.
Well, I already have null-modem, even wireless null modem using bluetooth, any of my Amiga systems can connect to a linux box with bluetooth, that offers PPP and shell login. But working over the serial line really sucks CPU and is very slow. Currently, the best ways to connect a Pi right now, is ethernet, using either PCMCIA or Plipbox. The serial is ok for having the boot console of the Pi though, and "light" data transfers now and then.
I'd probably start by exchanging input events between the two machines so that a USB keyboard and mouse attached to the Pi can generate input events on the Amiga.
I think that is possible already, I did something like that 15-20 years ago, and I suspect I was using this...
http://aminet.net/package/comm/tcp/netinput37.3 