Just out of curiosity and security test, i copied my own browser's cookies to another pc on same browser and surprisingly i managed to open facebook and google accounts with existing sessions even after public ip changed!!
Imo, it would be more secure if websites was clever enough to detect you r accessing an existing session from same platform/agent but from a combination of different ip/mac/machine model/unique id etc. in this case even if sessions stolen, only combination of same platform/agent/ip/user/any unique id that is related to actual user would be able to continue existing session. wouldnt it be good protection againts session hijackings? cheers