I think CAT1 REVERSION's first point is important. Experience has shown that, despite how simple it sounds, there are many incidences (and at least one accident) where RAs aren't followed properly. There are a number of EUROCONTROL papers, I think from the same series as posted, detailing mistakes that were made. A concern is people overshooting the green zone and causing another conflict with somebody else.
Acquiring the target visually gives the pilot a spatial picture of the situation, with ranges and bearings, so that the pilot is in the same mindset as TCAS, which probably leads to more confidence in the RA, and better execution.
Current traffic displays are bad at this: a 2-D snapshot picture of a inherently 3-D plus time conflict. Also, check out the new Airbus auto-TCAS system, which got recently certified.