CB,
Notice you still haven't quoted what yout manual actually instructs you yo do in response to an R/A.
Yes, TCAS is a boon and a suplement to the obvious limitations of see and avoid.
It is NOT a catch-all panecea to be used as a total solution. An R/A means every other source of avoidence has failed.
Too many are under the impression they are not allowed to avoid a collision unless the magic box tells them to do so.