> signed data include session id that is derived from result of first DH key exchange and thus unpredictable to either side of connection

The unpredictability of DH output depends on the group parameters and public key validation performed by the peer. If the group contains small subgroups, Eve can send an element of small order and predict the DH output with high probability.

For example, this is one of the attack vectors for the triple handshake attack on TLS: https://www.secure-resumption.com/tlsauth.pdf.