I don't think PPPoE uses IP...
isp home modem router . . . . . . . . . . LAN ADSL \\ \\ . . Ethernet . . ethernet PPP ---------\\ \\------------ ------------- --------- IP --------------/ /--------------------------------- | ================/ /=================================================== -------------\\ \\---------------------------------- | ---------\\ \\------------ ------------- ---------- . . . . . . . . . . . . . .
IP isn't the only network service than can be provided over ethernet or over PPP for that matter. Often (but not always) a device that combines the modem and router is used. Using a separate modem can reduce hardware cost in extreme situations where cheap modem/routers get "gummed up" and need to be reset. We had a modem-router at work that would stop accepting inbound connections at random times, we switched it to modem only mode ("passthrough") and used a linux box to do the ppp and router function. Reliability has improved.