MitM with regard to unauthenticated clients
but can pretend to be the client and see what the client is sending

No, the eavesdropper can't see what either side is sending except the ciphertext and size of the ciphertext.
To eavesdrop on any connection where the server is authenticated, the eavesdropper has to be able to convince the client that he is the server, which the eavesdropper cannot.

Doesn't that mean the server might be talking to an eavesdropper who inserted himself in the middle

Any internet middle box can do that.

and the eavesdropper can't decrypt server responses

True, and the eavesdropper can't decrypt client requests either since the eavesdropper doesn't have the session key.

but can pretend to be the client and see what the client is sending

Again, the eavesdropper doesn't have the session key, he can't do that.