It's connected because you judge it's absence from the equation as a connection, as i just said it just make the problem even more complex to balance because it's adding another variable to the equation.
Then after that they might be problem with lord defecting because they don't have enough fief, the impossibility to pass some kingdom policy or lord not joining armies anymore, i'm not saying it's going to happened, i'm saying that it might. Due to the fact that lord are unhappy about not having fief because you're bound to have more than some of them, and lord hating each other for the same reason.
Imagine having a lord loosing it's fief, then boom you suddenly have far more town than him, so he defect. So you lost a fief and you lost a lord for no obvious reason.
While for the influence penalty, it will either work or not work. But not causing additional issue that might need to be fixed later.
I'm wont defend that option more than that because i have no clue if it will be a good solution or not until it's implemented or tested, but saying that it doesn't make any sense is a bit overboard.
But isn't it possible to imagine relations mechanics that would largely by-pass problems with the influence equations (and thus influence-fief-gold snowballing), not complicate the same equations?
E.g. Sessession: If a lord, with fiefs, increasingly didn't like the faction leader, he could secede with his fiefs. If multiple lords didn't like the faction leader, they could conspire and secede together. (The lower the relations score, the higher the dice roll chance of this kind of thing happening.) If so, you would just need to figure out how to put negative ruler clan - vassal clan relations pressure on the ruler clan that would scale the bigger and more powerful the rulers got. (Also, generally, there would have to be be a larger suite of actions that impacted relations positively or negatively so that the player could, with difficulty, potentially manage this new pressure in their new kingdom.) That wouldn't solve the underlying influence bloat - fief bloat - influence bloat dynamic directly, but it would help a lot indirectly by just by-bassing the worst end-state iterations of the influence gain equations. (Because it would be way less likely that any one clan could get so many fiefs in the first place, especially for an AI, w/out fighting a secession. In this context, remember, we are viewing fiefs as influence-farms.)
All of this could work in some form at the intra-clan level, but I feel like it would be smoothest to implement at the kingdom-clan-fief interface level.
(To me, this is such an obvious idea that I have to assume that the devs are already considering it in some form. I ain't no genius! )
Edit: To be clear, relations management is already a minor thing in the game, yes. But a) It is not super impactful in most instances, as most lords with fiefs like you well enough specifically because they have fiefs, so only pathetic little clans defect, which is less significant. b) The influence cost of buying relations does not scale but rather costs a flat amount, more or less, so it's easier and easier to get better relations to bigger you get. It does make sense, of course, that more influence should buy you better relations. But if influence gain is unbounded, such that influence costs do not scale with size while influence gains do scale with size, then relations bloat is the natural result. c) There are generally too few things that alter relations in the game one way or another, and almost all of them involve the flat influence costs described in (B).