暗号化のアルゴリズムの使い方

I am confused as to why RSA public key encryption is not intended to be used for data. It seems that, instead, it is used to encrypt a symmetric key used in another encryption algorithm such as DES. The data portion of an RSA encryption block is up to 30 bytes, per the PKCS#1 spec. Why couldn't a message be broken up into 30-byte pieces and encrypted with the same key, as it would be using DES? Does this make the key easier to guess, as the same bit sequences are applied repeatedly? In DES, the key schedule permutes the key bits in each round, but the same key is used for every block, just as it would be in the RSA scheme above. Thus, I do not see what is gained by involving a second encryption algorithm. If RSA were slower, this would make sense, but I am not sure how a single exponentiation (C = M^d mod N), albeit one with a 1024 bit modulus, is slower than a 16-round algorithm in which s-boxes, etc are used in each round.