Agreed with above, by far my best Hard runs (as well as my first ones) were with me flying a heavy gun ship and carriers just as support (although contrary to above I did use upgraded missile boats and find them very effective, but by end game primary dps/alpha was beams/megaplasma by far so I should have probably just swapped to repair but couldn't even be arsed since I was in no danger anyway with proper positioning).
An additional issue with heavily fighter-dependent DPS is it dramatically increases the risk, particularly early game, of bad rolls in terms of environmental hazard systems. You can be going along and find a blackhole choke point, and suddenly your fighters are all popping before they can even make it to the enemy. Something a capital with some decent primary weapons could muscle through fine becomes grueling, particularly if/when there are no stations nearby and a constant stream of reinforcements. Even asteroid systems can be an issue if you've got bad luck.
And of course, fighters can often be really, really stupid and die barely doing anything but blocking some shots.
So ultimately I can see how a max count of upgraded ones could ultimately overwhelm a lot of this, but it seems like they're fundamentally just less reliable overall, and if you build your fleet around them then a bad fight could go really bad. It's game over if your ship dies really, I've never found an escape pod to be even remotely worth the loss of an entire weapon slot, particularly because by the end the loss of your primary ship represents an immense destruction of scrap/upgrade resources/lucky weapon finds over the course of the game that pretty much is impossible to reasonably replace, so you're toast anyway. Better to just not die at all.
Trying a max bomber run sounds like a fun challenge though and variation.