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.
I was contemplating going here (active detection range fall-off as the 4th power, rather than the square of the distance), but didn't because my recollection is that it's more complicated than that. But now that someone's opened the can of worms....
The 4th power thing is for diffuse reflection - if I think of the active emitter as a light bulb, then the reflected radiation from the target is acting as another light bulb, emitting in all directions. The power of the target light bulb goes like 1/r^2 (amount of light falling on it from original emitter), and the travel back gives it another 1/r^2, for a total of 1/r^4.
The problem is that there's also a specular (mirror-like) reflection component. First, imagine the target is a mirror oriented perpendicular to the path from the original bulb to the target. If you trace the rays, then you can see that they keep diverging at the same rate as if no mirror were there. So in the reflective case, the distances add (rather than multiply as in the diffusive case) So for the specular component, the fall-off will be 1/(2*r)^2. This effect is suppressed, however, because the active sensor has to "get lucky" and catch the glint of reflection off the mirror. This is why concave cubic corners are so bad for stealth - they reflect rays back no matter which direction the ray is coming in at. In fact, I remember reading that ocean-going small craft typically mount radar reflectors that are just corner-cube boxes - the idea is that you want a big freighter about to run you over to get 1/(2r)^2 power no matter how your boat is oriented.
Note that ESM will still have a big advantage over active sensors, because even though there's a 1/r^2 component to the active signal, it's still going to be suppressed by geometric factors in the target-emitter geometry. So while I agree that overall it should be MUCH easier to pick up an active signal with ESM than for the active signal to actually see anything, the active range fall-off is much more complicated than one might think.
On the whole fire control question, I don't think it should be any different than actives. Unless the beam is perfectly collimated, it will still have an opening angle, and so its power density should (eventually) still drop off with range like the distance squared. This behavior should kick in when the beam has gone far enough so that it's significantly larger (e.g. 2x) than the original aperture. The question is "how big is the spot size vs. the original beam radius for fire control at typical engagment ranges".
John
