As a malicious middle man, Mallory cannot alter H(M) because it is protected by Alice's signature. Therefore, the integrity of M is preserved by the hash function H. Moreover, Mallory cannot pretend to be Alice because he cannot construct Alice's signature.
Digital signature works well if the broadcast message is small and is completely known at the time of broadcasting (so Alice can compute the hash). However, messages such as video streams or live stock quotes do not fit well with conventional digital signature. As a replacement, we can use the stream digital signature as introduced in [GR97].
This architecture is described as a broadcast application. However, we can easily translate the architecture into a multicast application, where a member plays both roles as Alice (the sender) and Bob (the receiver). The main problem is when the multicast group gets very large, each receiver must keep track of all the public keys necessary to authenticate all the senders in a multicast group. Moreover, this architecture fails to address some other important properties such as sender authorization and confidentiality.