By definition, knowing the IP of a residential connection in absolute terms reduces privacy to nothing...
What I had in mind is not exactly privacy. Recently a user asked (not here) how his ISP would know that he had been participating and causing peer-to-peer traffic (they wanted him to stop). Here're some possible scenarios:
1) They just bluffed and notified him due to simply high traffic
2) They have DPI (deep packet inspection) and analyzed traffic to find BitTorrent protocol signatures. However this equipment is expensive to route all traffic through it; alternatively it was done manually in his case after point 1.
3) They analyzed this user's DNS requests (default goes through your router straight to ISP and is logged)
4) Reverse DNS lookups similarly end up on ISP's DNS servers. If you combine this indicator with high traffic, this is pretty conclusive then.
Personally I'm on the fence about it.