The problem with shooting over significant light-lag distances isn't that the target sees it coming and dodges, but simply that they maneuver unpredictably and as a result are impossible to hit with any sort of reliaility. TN ships move millions of meters in 5 seconds, and (in gameplay) can reverse course within that timeframe. So the evasion envelope over 5 seconds is vastly larger than the ship is.
The beam fire control range drop-off math doesn't make any kind of physical sense I can come up with. It's just a conveniently simple game calculation.
The game definitely has room to become more realistic and complex, and this is a step towards that. If random maneuvering is what ships use to dodge shots now, and we can still hit them, then there is no use on talking about what if they maneuver even more over a longer period of time. Just drop the hit chance harder. This is why I suggested multiple shots increasing hit chance. If I had to shoot at something that has 5 seconds to dodge and is moving erratically, I would use a
lot of bullets. So one shot could have 1% chance to hit. The second have 1.1%, then 1.2% or something like that (probably with diminishing returns). So if you fire 100 shots at a ship, you get far more than than the 63% (99% chance to miss 99 times in a row) chance to hit one shot, because dodging in 15 different angles is still going to get you hit by some of the shots.