Considering the amount of data used for internet, I think serial port on Amiga (max 19 200 bit/s) is simple not good enough. A side effect is higher CPU demand.
Do you think that the serial port speed would usually have been an internet connectivity bottleneck in the early 90s? 19200 bps is not the limit, by the way. I guess it depends on the CPU/DMA load, but I can for example use stable MIDI (38400 bps) on my 8 MB fast RAM A1200. I'm sure you can on a stock 500 too.