Each node on the network does not have a complete map of the network, so cannot determine the shortest path. And if the shortest path is chosen by everyone it will become congested. This is essentially the main problem with all Internet routing. Because of this, network operators share information about the path taken by packets they route, and which packets they want to receive to control congestion. When they receive a packet they use this information to determine a best next destination. Since all sources on the Internet cannot practically share this information, source routing is at a disadvantage. And attempts to discover short or fast paths result in added network traffic contributing to congestion.
In addition to the basic routing issues, source routing presents DDoS and 2-way spoofing attack vectors. You can spoof a 2-way conversation because destinations will take the reverse of the packet’s route. Eddie pretends to be Bob talking to Alice and crafts a path so that Alice returns communication to Eddie, thinking she’s talking to Bob. This is a major security vulnerability with source routing, which requires the use of encryption to prevent.