Okay, I'm a long-time corporate player so I appreciate this analysis, and I'll throw in a few thoughts.
Corporate activity has generally been pretty volatile, and there traditionally hasn't been any clearly determining factors for which specific corporate factions flourish and which do not. Over the last ten years, the most overwhelmingly active corporate faction was IMG, but that was primarily due to active leadership and recruitment, not due to any great advantages in the ID.
Indeed, there have been periods of dominant activity by corporate factions with objectively bad IDs with no mining and suboptimal rephacks, such as Planetform.
Rather than there being anything inherently wrong with corporate IDs, I think the two main reasons why corporate factions struggle with activity these days are economic: Ultimately, even if a corporation is playing militantly and engages in piracy and combat, most people looking to join a corporate faction will do so primarily to make money, and the bulk of faction activity for corporations will almost always be trade.
The two reasons why this has become a problem are as follows.
One, PVE is generally more viable as an income source. It pays more and is more engaging as an activity. And two, there's a lot less need to make money. Partially, this is because a lower proportion of the playerbase is new and in need of money, and partially this is because a fully kitted out capship costs 703 million credits less than it used to. (Edit: Although far less important, it's worth noting that snubs are also much cheaper to make these days)
So if you can make money faster by doing PVE, and you don't even need that money anyway because caps are so cheap to make now, why bother trading? You're only doing it for the RP, and that's not going to be enough for a lot of people.
This has resulted in a game environment that simply doesn't have trade as an activity focus anymore. If you browse the playerlist, you'll probably see traders on it, but almost every instance of an actual group that's doing a group activity will be either roleplay or combat. The cycle then perpetuates itself: You'll look at the list and think, hm, I could go trading. Alone. Probably not even encountering anyone. Or, I could log a ship to roleplay or shoot people, which has a far greater chance of meeting that goal.
The IDs are generally fine, although I would like to see more generous piracy lines on corporate IDs. "Can engage in piracy against non-allied corporate ships outside of house space" could be put on every corporate ID. And their engagement lines could be made more generous as well, with "ships belonging to factions considered hostile be [house]" being replaced by "hostile to [faction]", which could make it easier for corporations to log for combat if they have active enemies.
But overall, the problems corporations are facing are due to other factors not related to them directly.