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I am trying to understand the proxy re-encryption scheme.

In proxy re-encryption:

(1)Alice use AES key to produce the symmetric ciphertext of her message.

(2)The proxy encrypt symmetric ciphertext using Alice's re-encryption key.

(3)Bob use his private key to get the AES key and decrypt the symmetric ciphertexts.

My question: Why we need the re-encryption? Why not Alice encrypt her AES key using Bob's public key and send it to Bob?

I am new to cryptographic, so I am not sure misunderstand of it. Thank you!

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