When radar positions are band boxed, the ATCO is doing just the one job. Granted that this is in a bigger area, overall, than if he is controlling just one sector, but it is still just one piece of airspace & his attention is not being distracted by events outside of his area of responsibility. But, IF an ATCO is controlling more than one aerodrome this involves him doing more than one job, & he might very well be distracted by events in his other area of responsibility.
In my view, you cannot compare band boxing of radar sectors with an ATCO doing Aerodrome Control simultaneously at more than one aerodrome.