I'm not sure that AP, even AP trading, is the problem - or, at least, it may only be a problem because of an overarching other issue: Lack of scarcity.
Silver and resources are effectively unlimited resources, really gated only by skills (which can fairly easily be pumped through activity + rs-hunting + teaching), and when they're acquired, can be turned into sort of an escalating feedback loop pretty easily - you can't trade AP right now, but you can still hire a haggler, or tap a protege, or buy raw resources/silver from someone who has nothing better to do with their time than generate it.
But that silver and those resources don't come from anywhere. Acquiring them has no opportunity cost or consequences, and they don't really represent anything real in the world. "Economic resources" don't reflect the wealth of a land that can be drained, they don't represent contracts with craftspeople who can be fully booked, even when it would make sense. Same for military (where do those new soldiers COME from? What isn't getting done on your lands because you decided to turn a thousand peasants into soldiers?), and even moreso for social. I think that feeds the playerbase's inclination to see acquiring these things as just a matter of "running code" rather than as IC actions that reflect things their characters are doing offscreen, things that matter.
And I think that sort of plays into a lot of the other issues - prestige balloons because people have effectively infinite resources to plug into chasing prestige. Investigations can be pushed along quickly, burning through clues, because dumping 50 resources every week isn't really that big of a deal, especially if you have two or three people helping you out. There's not a lot distinguishing non-leader nobles and commoners because there's no tension between them - and no pressing need to expand one's lands to grow, so no reason to not be friendly, diplomatic, and cooperative (which also contributes to resource/wealth/prestige bloat, because you only have to think about defending yourself from NPCs and not from hungry, hungry neighbors).
I remember, early in beta, staff talked about wanting to make sure that the wealth reflected in the world came from somewhere, that it could eventually be traced through the whole cycle. I feel like, in some ways, that's become a larger challenge as the game has expanded - in the rush to ensure that everyone has something to do, the coupling of 'thing to do' and 'what this means in the world' has been strained.
Unfortunately, the solution that comes to my mind would be a near total rework, and everyone would hate it. So I'm not sure what a GOOD solution would be, but I think it kinda has to start with looking at 'how much wealth, in silver AND resources does the Compact actually have and where is it', and reset things to reflect that, with systems that allow slow, risk-having growth (like conquering Abandoned territories (or your neighbors)), but fewer that just create silver/resources/materials out of whole cloth.