I'm guessing that this effect would have a negative affect on gameplay, however for completeness sake I want to point out that while passive sensors should diminish in ability based on the second power of the distance, active sensors should actually diminish with the fourth power of the distance.
That is because they emit a signal which degrades with the second power of the distance, and then that signal hits a contact and reflects back, and that reflection also degrades with the second power of the distance, so the total degradation is the fourth power of the distance.
If this change was made in the game the result would be that it would begin to become nearly impossible to scan an enemy with active sensors without him seeing your active sensor signature (right now it's unlikely in most cases, but a moderate tech advantage can give you that scenario for typical ships with small EM sensors).
As an example, if you increased your sensor strength by a factor of 16, you could only see twice as far as you could before, however your enemies can see you 4 times farther out.
I would still model Fire Controls as diminishing with the square of the distance however. Those aren't area sensors, they are only monitoring a single target, so that fixed beam on the way to the target wouldn't lose strength over distance. Once the signal does hit the target, however, the reflection would begin to disperse normally.