Bob wants to encrypt a message and send it to Alice using Alice's public key. However, Bob also wants to sign the message using his private key before encrypting the (message + signature).
For sake of argument lets assume Alice and Bob are using RSA2048. According to PKCS #1 v2.2, both, RSASSA-PSS and RSASSA-PKCS15 signature schemes produce an output the size of the key's modulus (in this case 256 bytes). However, both OAEP and PKCS15 encryption schemes require the message size to be less than the modulus size (less than 256 bytes).
How can one sign and then encrypt a message according to this spec? Would the plaintext just be broken into two chunks? Hybrid encryption seems like overkill if the message is small. Even a single ASCII character would be too large to sign then encrypt this way...