Hehe, and I didn't want to sound like I thought you were questioning .
I can try explaining a little bit more.
This is the gain pattern for four antennas (as in the F-14) in the horizontal plane, assuming that the airframe doesn't interact with the signal. I created it today from the model we use. Each antenna is represented by a different colour.
As you can see, there are some overlapping regions, but they are not huge.
Let's take a look at two extreme situations.
1. The signal is coming from the straight ahead.
Let's look at the point marked as A). The red antenna and the blue antenna are the same sensitive to that direction, and the gain value is good. The other two antennas, point B), are almost completely blind to that direction. Effectively, we can use only two signals - red and blue.
2. The signal from 45°.
Now, three antennas can see the signal. The blue antenna is at its maximum. The red and the green - C) - are of the same magnitude, although much lower than the blue (the plots are in db, so log scale... the red and green are ~50 times lower than the blue). The fourth antenna is completely useless in that direction.
It could be possible to use the blue, and both the red and the green for the grey area. However the area is small and adding another signal of such small strength, and thus low signal to noise ratio, may not necessarily improve the precision significantly. On the other hand, as mentioned above, it would require more CPU power. Concluding, the result may be not worth the effort.
Radar warning receivers aren't sophisticated ELINT devices. They are to warn the crew that there's a threat that can kill them, and inform about where the crew should roughly look to find a bandit or incoming missile. There is a trade-off between the precision and a set of factors as costs, weight, structural demands, etc. We may question the choices of the engineers and the customers (NAVY), but we have to live with what we have .
Side note: The world isn't 2d, each antenna has a similar pattern to the patterns from the included graphics in its vertical axis (both in real life and in our model).