The problem is that RSA is somewhat unusual in that it does not really distinquish between public and private keys and the primitive operation is invertible by

The problem is that RSA is somewhat unusual in that it does not really distinquish between public and private keys and the primitive operation is invertible by doing the same thing with the opposite key. That means that encrypt/decrypt/sign in the textbook aproach are essentialy the same primitive operation and verify is trivial extension. For most of other asymetric algorithms the primitive operation is DH-style key agreement function and the derived encryption and signature constructs are significantly more involved and in fact there isn't that much of an symetry between them. (and also the plain asymetric encryption operation gets somewhat pointless)