For System 7, Speed Double 8 when installed as a full package will display file transfer speed, although I can't speak to, the, uh, veracity of those measurements. I've only ever done this on PowerPC though. (overall the main selling point of SD8 is to replace the 68k emulation code so it's primarily PPC targeted but the other functions it does have might work on PPC, there's also a server component which I've laid eyes upon but never tried to use.)
Unfortunately, I don't believe it records a history and calculates a final average overall speed. That might be doable with IP-based software using MacIP, but that's very much entering into a different era and sort of getting into a different set of potential requirements.