Each and every communication pair should have unique shared key to achieve a good security level. The required no of shared keys is the major problem that symmetric cryptography faced. Another important problem is sharing the secrete key between communication parties.
Even though this has some drawbacks, computationally symmetric cryptographic algorithms are much faster than asymmetric algorithms. Thus people more like to use symmetric algorithms than asymmetric algorithms.
There are mechanisms which use asymmetric cryptography to only share the symmetric key once. Then once key is shared, sender and receiver can securely send data on public network.
Even though this has some drawbacks, computationally symmetric cryptographic algorithms are much faster than asymmetric algorithms. Thus people more like to use symmetric algorithms than asymmetric algorithms.
There are mechanisms which use asymmetric cryptography to only share the symmetric key once. Then once key is shared, sender and receiver can securely send data on public network.