A reason why symmetric cipher is the keystone of cryptosystem:

The symmetric and keyless algorithms tend to be the workhorses of the crypto- graphic world. As we move from keyless algorithms to symmetric algorithms, and on to asymmetric algorithms, the algorithms at our disposal tend to be slower. An old rule of thumb used to be that a block cipher might be around 50 times faster than an asymmetric algorithm, a stream cipher might be around twice as fast as a block cipher, and a hash function might be faster still at around three times the speed of a block cipher. However, current design trends in all three fields, block ciphers, stream ciphers, and hash functions, are providing more and more exceptions to this crude comparison and it shouldn’t be relied upon too closely. However, it does at least help to set the perspective with regard to symmetric and asymmetric cryptography and it illustrates why we leave the bulk data processing—for both encryption and authentication purposes—to the symmetric and keyless algorithms. ~[from"The block cipher companion"page.3_{page.3}]