Wow Phone Man sure brings back memories.. I missed out on blue boxing, though, in my area, but it still came in handy by handling different bits/stop bits/etc. I never used the host mode (only vaguely remember it, actually) though I remember a lot else about it.. The "Motor City Madman" wrote it, yes? I digress.
All my experience with BBSs were one of two types, and neither like you describe. Either P/D and if there was a limit, it was just to let others call in (like being able to download only X files a day, or only being able to be on an hour a day, etc) and the other would be for warez that didn't usually have a time or file limit, but a credit limit. You had to upload X amount to download Y amount.
On the Amiga itself, the most popular for warez was AmiExpress (I'd certainly guess anyway) (Often written /X, btw) and that was slimmed down as far as a BBS goes and file transfer oriented but, again, not at all like a single password ftp-like program. I think the popularity of the Amiga (and C64, the other computer I traded heavily with) made keeping tabs on downloading a priority. (Read: Lots of leaches.)
Having said that, perhaps a scene group may have set something like that up, but I was never in a group.
I don't know what you mean by a "disk communicator". To take a stab at it, though, DMS (Disk Masher, or Smasher, or.. something) was used heavily for trading and warez. A PD application to just compress a disk (a disk entirely, not simply the files on the disk, which meant some non-standard (though not protected) disks could be transferred) but it also allowed for a little text to be shown before unpacking which was used to have an ANSI group logo, BBS numbers, etc. That would be the closest thing I know of on the Amiga for what you're talking about.