This talk of "it's as fast as the parallel port it uses" are a bit vague.
While all "built in parallel" Amiga ports are bits of complex interface adaptor design, how they are read and written is in part down to which software driver the pilipbox is using.
I would guess you get about 25KB a second maximum, but that's kilobytes per second. So not too shabby.
The hardware latches on 8520s will work reliably at 56K, but how close the various releases of driver have got to that hardware limit, I've never tested. 1.3 versions of parallel.device were very iffy and clumsy IIRC. Presumably later ones are faster and more reliable.
Some Zorro cards have much faster parallel ports than the standard, obviously, which might outshoot the average 10Mb (Megabit) per second Plipbox. That would to a certain extent still depend on the processor of the Amiga used. For instance an A2000 is still a 7MHz computer even with a very fast Plipbox and much faster parallel port.