I think that destroyers do have their place as a way to fill out fleets. To form up battle lines and support your cruisers and capitals. For example, early game hammerheads are flat out the best anti-destroyer destroyer in the game. Late game, they're great line ships that can tank and do damage to cover the flanks of larger ships or protect glass cannons like sunders.
However, this thread did bring up some interesting things about frigates vs destroyers. That is that they're are very few rare/special destroyers in the game. The frigate class has the hyperion, scarab, tempest, monitor, and omen ships. These are all rare ships that players rarely use in early game fleets, but generally phase out their early frigates in favor of them in the late game. The destroyer class doesn't have many of those, only the medusa and manticore. The medusa is generally seen as undertuned at the moment, leaving the manticore as the only rare destroyer that has real universal appeal for its ability to add serious firepower to a late game fleet for cheap (similar to the sunder, but that's a more common ship). If all you had for true warship frigates were the lasher, wolf, brawler, and vigilence, I think a lot more players would also drop frigates entirely from their fleets.
So I don't think the problem is that the destroyers are innately bad, it's that there aren't any crazy end game ships in the category like frigates that give players strong reasons to keep using them.
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A lot of people have mentioned the officer bonuses not applying to destroyers, I kinda feel eh about that. You have to account for the fact that a destroyer has higher base stats and more weapons than a frigate does. So the officer's base skills apply larger bonuses to those. The larger bonuses to frigates specifically is to offset that innate advantage of putting an officer in a larger ship. If the frigate bonus wasn't bigger than the destroyer bonus, it'd always be better to put those officers in destroyers.