Upon inspection of the codex, the one campaign stat where Onslaughts (and Legions) have it the best is CR per deployment. Assuming officer and fleets skills so you're starting at 100%, 20% for Paragons and Odysseys means after 4 deployments in quick succession, you're suffering malfunctions. 15% for Conquests and Astrals means after 5 deployments in quick succession, you're suffering malfunctions. Onslaughts and legions can go a full 6 deployments before starting to suffer malfunctions. In addition, Onslaughts and Legions recover a single deployment's worth of CR in only 4 days instead of 5 for the other capitals.
Or in other words, they're reliable and don't break down as fast as high tech ships in stressful campaign situations. It admittedly rarely comes up, but there are situations where its handy, such as raiding a heavily defended system like Askonia. Or taking 4 Ordos one at a time.
And while people always complain about the flux dissipation of Onslaughts, their flux stats are not that bad, especially with fleet skills in a campaign. A paragon costs 60 DP, and assuming Loadout Design 3 and no officer, caps out at 2000 flux/second (1250+150 flux distributor+600 vents), or 33.33 flux dissipation per DP. An Onslaught caps out at 600+150+600=1350, or 33.75 flux dissipation per DP.
A conquest admittedly clocks in at 1950, or 48.75 per DP, but at the cost of taking 40% more shield damage than an Onslaught, or 133% more damage than a Paragon. Odysseys are actually in an interesting place at 1750, or 38.88 with Onslaught quality shields.
So in a typical campaign build, Onslaughts bring just a smidgen more flux dissipation to the table than Paragons in equal DP numbers. Given that Onslaughts have 360 OP, and Onslaught XIVs have 370 OP, there is no reason to not spend 80 OP on max vents and grab a flux distributor. So for most player characters fleets, Onslaughts don't seem to have terrible flux stats to me.
The problem with Onslaughts is they have so many mounts it is way too easy to over gun them. Think of it this way: Odysseys have three large gun mounts (for 45 DP), Conquests have four large gun mounts (for 40 DP), and Paragons have four large gun mounts (for 60 DP). Onslaughts have five large gun mounts (3 ballistic, 2 thermal pulse cannons). If you equip Onslaughts like they should only have 3 large gun mounts (2 thermal pulse cannons and 1 large ballistic), you're equipping it like a paragon in terms of large weapons to flux dissipation ratio. 2000/4 = 500 flux per weapon. 1350/3 = 450 flux per large weapon
You can also consider the smaller mounts. Value small mounts as 1, medium mounts as 2, and large as 4. With this valuation, Odysseys have 24 units of gun mounts, Conquests have 36 units of guns, Paragons have 37 units of guns, while Onslaughts have 44 units of guns. I'm ignoring missiles since they don't produce flux. And in the Onslaught's case, all but 2 guns face somewhere in the forward 90 degrees. So in a typical engagements, they can bring 40 units of those guns to bear. A Conquest in a battle line only brings to bear 20 units worth of guns in comparison.
Given Onslaughts are way over weapon mounted means you typically want less damaging but higher flux efficient weapons, or want to equip smaller weapons (small in a medium, or medium in a large), or even just leave them empty. This is why Onslaughts are the king of point defense. Ballistic PD tends to be flux efficient, and the Onslaught has more mounts than any other capital.
Although, I think the simplest answer is they work well enough at vanilla end game and they're easy to get. Given its a single player game, that seems fine to me. They're not the best capital (mobility system only goes forward, slowest capital going in reverse, no fortress shield). However, when outfitted properly, they put out respectable damage, and can absorb amazing amounts of punishment over the short term, second only to a Paragon. And in fighter or missile heavy situations, potentially more.