Often data is encrypted using Symmetric Ciphers and Symmetric key is shared with recipient by encrypting it with recipient's Asymmetric Public Key. NIST Special Publication 800-56B, Revision 2 section 9 defines RSA KTS-OAEP to establish keying material between sender and receiver. Is it really necessary to use RSA OAEP or RSA KTS-OAEP to establish keying material between sender and receiver?
Since most of the time, symmetric key length is much smaller than asymmetric key length e.g 256 vs 2048. Is it safe to use the textbook RSA to encrypt the symmetric key in a scenario where new symmetric key is randomly generated by the sender for each message?
Since randomly generated symmetric key is not likely to repeat, there is no need to use RSA OAEP and RSA KTS-OAEP?