but changing frequency, talking to ops/company, dealing with the CC, selecting flap, being alerted to wayward trends, reading the QRH, etc all mean the fellow may easily miss is quick stab of a button on the MCP.
...and the solution to your example of an overloaded PM, is to give him more stuff to deal with by requiring him to acknowledge a callout?
If I'm particularly busy (which your example isn't), I expect the other guy to focus on the flying bit, and leave the rest to me. If I'm ever wondering what the plane is doing, I can look at the FMA and question anything unusual. We have a master warning sound, and a master caution sound. No need for my voice to be the master normal sound.