The regular telephone network doesn't have the notion of packets and lives just fine. ATM has fixed size cells without self-contained addresses in them and it manages to work, at least sometimes. MPLS uses labels in its frames and works. But IP carries information in packets .
Packets are arbitrary sized chunks of data an internet can deliver.
Logically, higher-level protocols are layered on top of IP and abstractions such as a data stream are created. But in the routers and on the wire what we have is a bunch of packets.