I reckon if you can't take 1 second to transmit 'TCAS RA' and continue to monitor the PF's flying then you're in the wrong job. Amazingly, depsite many of us not being female, we are able to do more than one thing at a time and looking at the appropriate instruments (with our eyes) and talking to ATC (with our mouths) is really quite easy. There really are far too many precious people around trying to make mountains out of non-existent molehills.
I've had 2 RAs. They were not high workload at all. In both cases the warnings were reacted to smoothly and accurately and the whole thing was a total non-event. By the time the PF had disconnected the autopilot the PNF had made the call. No aircraft doing aerobatics because PNF wasn't monitoring and really quite relaxed.
It is nonsense to suggest the PNF must spend every millisecond monitoring the PF and the usefulness of the call to ATC far outweighs the 1 second during which you might have to use a different part of your brain to carry out a different task.