A bitcoin address is created from an ECDSA keypair. It is common to use use a hashed version of the public key as the shared address, but the original bitcoin implementation also allowed for using the unaltered key directly. (which anyway is revealed when the coins in the address is spent) The purpose of public key cryptography here is that the owner can prove ownership of the address by a digital signature, which is required by the blockchain before accepting spending of the coins in an address.
The ECDSA algorithm is not suited for encrypting messages. If an RSA keypair was used it would allow the sender of money to encrypt and convey some personal information to the receiver (eg. by a public message server), which obviously could be a useful feature. Is there any reason why an RSA keypair should or could not be used for cryptocurrency addresses?