I doubt it is processing power limitation since during the search mode the whole beam is processed.
Hm the figures suggests you have a scanning beam: the radar can't observe the whole sky at once. So, until anything happens, you scan (as in: focus the beam at a spot, wait for the farthest sensible reflect, then you look at the next spot) the part of the sky from which attacks might be coming.
Typically that part of the sky is "empty", there's not going to be civilian aircraft in there, for example
Of course, once you detect something, you want to make sure where exactly it's going, and that it's really what you think it is. Hence, you shift your beam to a predicted position of the target. But that might include other radar targets – steel structures, your own aircraft, civilian aircraft, your own artillery fire...
So, it doesn't suffice there's something in your beam, it needs to be in the right spot.
Now, if you can't choose where you're looking, your SNR suffers – as said, there's clutter, there might be your own reflectors etc. So, this operation basically requires you to increase your radar's sensitivity by gating out anything that's not what you're expecting.