It could be argued that if played correctly the pitch change to react to the RA is gentle and not aggressive. In fact the FCTM states, in part: "RA maneuvers require only small pitch attitude change which should be accomplished smoothly and without delay. Properly executed, the RA maneuver is mild and does not require large or abrupt control movements. Remember that the passengers and flight attendants may not all be seated during this maneuver".
It takes only small manual pitch changes to cause quite significant auto-throttle movement if the AT is engaged. In turn this can exacerbate trim and stick force changes. In the simulator we occasionally see pilots flying a visual circuit by hand with AT engaged and it doesn't take long to see the AT moving up and down in response to minor speed variations caused by inaccurate height keeping. In a nutshell it makes for sloppy lazy technique.
There is one point to be considered in favour of leaving the AT engaged - despite the Boeing recommendation. And that is manual flying currency. With the almost total reliance on automation demanded by manufacturers, regulators and airline ops departments, pure manual flying skills inevitably decline. We see this when pilots disconnect the automatic pilot to practice an instrument approach.
Manual throttle skills degrade too - and that is understandable since autothrottles are used in almost every aspect of airline flying. Some pilots may feel leaving the AT engaged in an RA manoeuvre, is safer than leaving it to a startled pilot who is steeped in automatics is suddenly faced with manual flight and manual thrust lever operation during an RA. Of course for those pilots equally competent at automatics and full manual flight there is no problem with following the Boeing advice.
In a perfect world, all pilots should be equally competent at both automatics and manual flying skills. In reality, the increasing prevalence of Loss of Control accidents over the years, prove this to be far from true.
In my view, Boeing are right in recommending that manual flight means manual throttles as well.