I would say, however, that Large "Ships of the Line" should fear fighters. It makes sense that a large amount of fighters would have the ability to take out a large ship. Ship to Ship combat should be a VERY dangerous endeavor. The larger ships are equipped with fighters for the main purpose of taking out other ships and defending against attack. If you find that the flavor is lost, perhaps you could take the tactic of making the defenses better on the larger ships. It would make sense that the Flagship class of vessell might have extra shielding which would be represented by not making the shields ablative. A small merchant ship probably only has one shield generator as opposed to the advanced systems found on a Battlecruiser.
While I understand your concerns regarding the number of dice dropped in one of those massive attacks, I do not agree that by itself that would be a show-stopper. I think that if you are trying to have the flavor of your campaign be one of military battles in which the players are just part of the crew or line officers, then perhaps you should look into the damage classification system originally proposed.
In my humble opinion, Star Hero was created and intended for character driven story arcs, not massive space battles. Although it works in any scale and genre, if all you are looking to do is to have large space battles, perhaps you should look into other systems out there.
Personally, I love wargaming large battles using hundreds of minatures. But that is not what attracts me to the Star Hero campaign. If I want to have a war driven campaign, i would probably utilize a minatures based system like GW Battfleet Gothic.
I am currently co-GMing a Star Hero campaign in which the players have a ship, but I HOPE they do not try to go up against an Empress Class. (Hint to all of you in my campaign.) There are times to get into battle and there are times to accept the fact that you will be boarded.
Again, that is just my 2cr worth.