The real problem is that LRF are effective against too many different types of ships.
The LRF only counters capital ships and light frigates. That's two unit types, hardly an excessive count. Consider that the LF counters scouts, flaks, carriers, and support cruisers. The real cause of the LRF's strength are those raw combat stats. Simply put, the only unit that compares in terms of bang for your buck is the heavy.
Rebalancing the LRF to be countered by "fast and agile" units would probably be impossible without
completely rewriting the entire counter system, which would require
at least half a dozen iterative patches to get right. That's just not in the cards.
A second problem with increasing fighter damage is that this doesn't just punish LRF spammers. In fact, it punishes people who mix in small amounts of LRF more than it does the spammer. Think about it; if I have 80 LRF, you I can take a few losses before my DPS starts to sink dangerously low. If I have 20 or 30 LRF, you could seriously knock out that entire segment of my army before it fulfills its role as a counter.
I think that may just make spamming problems even worse. If you can somehow protect them, LRF are just as no less dangerous, but if you can't they're not even worth building because fighters can pick them off. This is already the case early game, where it's easy enough to suppress small numbers of LRF just using a carrier cap, which was my initial objection to the proposal.
To be clear: I am very much against any buff to fighters. The fighters themselves are fine; if anything it's the carrier cruisers that are weak right now. The fact that players are spamming carrier caps is indication enough that this is the case.
Now, one possibility to make capital ships tougher could be to rework shield mitigation. Right now, any realistic scenario will max out shield mitigation practically instantly. This means that focus fire is the best course of action; mitigation is already maxed, there's no further penalty to piling on more DPS.
My idea is to raise the maximum shield mitigation values, and also make mitigation fall faster when at higher levels. The result would be it will take a lot more DPS to max out mitigation. This means that there will be diminishing returns for focus firing a capital ship with your entire fleet. This would have the added bonus of not making capital ships any tougher in the early game.