This is a soft question. I don't know a lot about cryptography or its history, but it seems like a common use for RSA is to do key exchange by encrypting a symmetric key to send a longer message (e.g., the description of iMessage here). Isn't this exactly the thing that Diffie-Hellman key exchange, which is older (and to me seems simpler) is for? Looking at Wikipedia, they were also both patented, so this wouldn't have been responsible for the choice.
To be clear, I'm not asking whether it's theoretically important that public key cryptography is possible. I'm asking why it became a standard method in practice for doing key exchange. (To a non-cryptographer, DH looks easier to implement, and also isn't tied to the details of the group used.)