Range of Beam-Weapons (all non-Missile): This is mostly a balance issue and to make a meaningful choice between Beam-Weapons and Missiles .
You can't stop Beam-Weapons and Beam-Weapons have a lower logistic overhead.
If Beam-Weapons have a range comparable to missiles there would be no use for missiles.
There is a convenient limit (Min time increment) x (Speed of Light) to give a reason for the range limitation.
FTL Beam-Weapons would remove this convinient limit without giving a new limit
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Yes, this is exactly why the limit applies. If beam weapon range increases, they become too powerful and the 5-second limit is convenient technobabble. Currently, longer-range beams can be closed down by faster ships within a reasonable time. If the range noticeably increases, longer-range beams win regardless of speed.
Faster ships with longer-ranged beams win in either case.
The 5-second limit however does not apply for most of the game. That is 1.5M km, and early 4x range fire controls maybe use 10% of that. More to the point, nothing about the 5 second interval says that lasers/mesons/etc can only fire once per increment. Gauss cannons already do that, so there is no reason you can't have a 2, 3 or 4 second firing interval, which would result in more shots in some increments and less in others, as currently area Beam defense is rendered useless by 5 second increments. Similarly, there is a massive jump in beam damage output going from 10s to 5s fire rate, which happens at an arbitrary point in cap tech research, it would be much smoother to allow every upgrade in capacitors result in actually faster firing weapons.
Most missiles spend only a single 5 second in range, allowing only a single shot, which means you may as well use final defense.
The 5-second increment can be still kept, but instead each ship knows both its position last increment and the new position. The range for any shots fired can now be calculated by linear interpolation during that increment. So if you fire at 1st second and 4th second at a missile closing in at 30km/s, the first shot might be at 120kkm, the second at 30km/s.