Key exchange is done for speed (symmetric key crypto is way faster than public key) and forward secrecy. It’s not done because RSA is flawed per se. We use DH instead of e.g. ElGamal encryption for the same reasons.
Yeah it's not so much of a flaw of RSA, but encrypting pure text with it for example is more complicated (and has more caveats with padding, etc) than just encrypting a fixed amount of bytes
