There are many steps needed to understand the reasons and I will try to guide you through each.
1) Use encryption correctly...
With RSA algorithm, Alice and Bob can just share their public keys
(public_a, public_b) and keep their private keys (private_a,
private_b). Alice can just send Bob the messages which are encrypted
by private_a, and Bob can decrypted it by public_a. They can still
communicate over an insecure network, without Diffie–Hellman key
exchange at all.
That part is plain wrong. What you are doing in this part is signing, not encryption. Since public_key_a is public, your messages would not be encrypted at all. Instead of doing that, A should be encrypting the messages with public_key_b and then B can decrypt them with private_key_b. Since private_key_b is only know to B, A knows that only B can decrypt it.
Digital signature proves that a message come from a particular person. Encryption proves that only you, the key holder, and the person that encrypted the message, message sender, know the message. You need to have both encryption and signature when using asymmetric encryption. Encryption to protect the confidentiality of the message and signature to prove that you are the one that sent this message.
But, there is still more to it... For example, you still need to protect against replay attacks.
2) Bob usually doesn't have a public key
Let's say that Alice (A) is the server and Bob (B) is the client. Usually the client doesn't have a public key. For example, do you know a public key? The answer is most likely NO. Hence, Bob can receive message from Alice and verify that they really come from Alice but Alice cannot be sure anything it receives from Bob really come from Bob.
That problem is one of the root cause why we added key exchange protocol like Diffie-Hellman.
3) RSA is limited to one block.
There is a technique used to encrypt long message that is called cipher block chaining. Sadly, this technique cannot be used with RSA. It's not that it's totally impossible but rather that no one knows if it's really secure if we do it. Hence, it limits RSA encryption to one block. On the other hand, symmetric encryption algorithms like AES works like a charm with block chaining and is the reason we use them.
Further reading : https://crypto.stackexchange.com/a/126/16369
4) Diffie-Hellman is a key exchange protocol
Diffie-Hellman is just a way to "create and share" a key which can then be used for symmetric encryption. The
strength of Diffie-Hellman is that all the conversation to create this key can happen in plain text and the key
would still be private.
Note : Diffie-Hellman doesn't solve the problem of MitM attacks because it cannot authenticate the parties communicating with each other. This problem is instead solved with digital signature.
5) Ephemeral Diffie-Hellman provide Perfect Forward Secrecy
Ephemeral Diffie-Hellman is just a fancy name to say that you are generating new Diffie-Hellman key-pair every session and you don't store them. Since you never store them, an attacker can never retrieve them.
See this very good answer for more details : https://security.stackexchange.com/a/38142/50051
6) Ephemeral Diffie-Hellman protects you against replay attack
A very good side effect of using Ephemeral Diffie-Hellman is that it also protects you against replay attack. Since the server and the client is choosing a new random private DH key every session, you cannot replay the message from another session to impersonate the server or the client.
This is a very brief overview of how TLS works and all those parts are required to provide a secure connection. Without symmetric encryption you cannot encrypt long message and without asymmetric encryption you cannot share encryption key and provide perfect forward secrecy.