Is semantic security important in a hybrid cryptosystem?
Not a complete answer, but since you mentioned "unmodified RSA" I feel it's relevant.

Something stronger than vanilla RSA is necessary, even if it isn't semantic security.

Example: What if you have a public key exponent of 3 and the symmetric key being encrypted is 16 bytes long? Using raw RSA, $m^e$ would be about $128 \times 3 = 384$ bits long and thus smaller than any modern public key modulus would be. Being smaller than the modulus would prevent the calculation from taking advantage of the RSA Assumption, which is the premise of RSA's security. Since $m^e$ is easy to factor simply over the integers all security would be lost. (And this mistake would be somewhat obvious to the attacker because the vast majority of the high bits would all be 0.)