This whole dynamic of vassals demanding wars is just completely backwards to me. I can't recall reading about too many instances where unrest and rebellion (amongst the nobility) was caused by a king letting all his nobles get fat and rich off their lands, while there are plenty of examples of kings getting themselves mired in crisis because they kept the men out of the fields too long, or just got too many of them killed for some piece of real estate they were probably going to give out to their cousin anyway.
To my mind when discontent vassals decide they want a fight it should be a rebellion against their king not a war of aggression against a (usually) much stronger neighbour, and it should be determined by how prosperous the king keeps his realm, not by the fact that they have now hit clan tier 6 and obviously deserve more lands than there are in the kingdom. Then a good ruler would want to have periods of peace and would want to keep the enemy from burning every village in the realm fifteen times when wars do happen. I don't think the ai has any awareness that economic growth is actually a thing though, which would explain a lot.
I think your both right and wrong.
Where your wrong is that I am sure that if you looked at enough historical documents there would be many, many cases where a King or Emperor has been pushed into a war or peace because of internal pressure from his vassals or his governed people. Politics does happen even in the most strict totalitarian regimes. The big difference is that at the end of the day the King or Emperor ALWAYS decides and his decision in final. If he votes no, even if it makes his vassals or people unhappy, then the vote is no. No means No period. It doesn't happen that way in game though.
In game, a King has to use his influence to try to block a declaration for war but if he doesn't have enough influence, his faction will go to war despite his wishes and that leads up to where you are right. The King or Emperors decision should be final period. If he says no, then you faction doesn't go to war. Simple.
How it should work is if the Lords push for war, the King can then choose to just vote no ending the discussion there and take a relationship loss with those lords pushing for war or use his influence to mitigate the relationship loss. Either way the decision is final because he is the King after all. Obviously if the King runs out of influence and decides to keep ignoring his vassals desires, well eventually his lords will either defect or rebel.
As for influence, seriously, they have this all wrong in the game. Influence should always be considered just a numerical representation of a Lords powers of persuasion. He isn't buying shares, instead he is persuading others to agree with him. If the King spends influence to sway a decision, some of the lords opposing him should change their position or at least disagree with him less. For Example:
Lets say 5 lords want to go to war and all other lords abstain from the vote. Here are the five lords and their relations with the King.
Example A:
Lord A: Relation = 53
Lord B: Relation = 19
Lord C: Relation = -10
Lord D: Relation = -25
Lord E: Relation = 30
Vote = 100% go to war.
King votes No
Result of War Declaration:
5 Lords voted yes to war but vote overruled by King. No War Declared despite his Lords all support war because he is king and his decision is final. King loses relation with all 5 lords with the maximum loss of relation based on the lords starting relationship with King.
Relationship after vote:
Lord A: Relation = 53. Lord loses 2 = 51
Lord B: Relation = 19. Lord loses 5 = 14
Lord C: Relation = -10. Lord loses 8 = -18
Lord D: Relation = -25. Lord loses 10 = -35
Lord E: Relation = 30. Lord lose 3 = 27
Basically relationship with all the Lords go down but those more friendly to the King lose less relations than those unfriendly.
Example B:
Lord A: Relation = 53
Lord B: Relation = 19
Lord C: Relation = -10
Lord D: Relation = -25
Lord E: Relation = 30
Vote = 100% go to war.
King votes No to war but uses 100 Influence to "Sway" opposing lords to his side.
Result of War Declaration:
Influence sways the vote of Lord A and Lord E due to high relations and a high amount of influence used. Vote changes to 3 for war, 2 against war. The result is no war because King opposed the war and his decision in final. No relationship change for Lord A and Lord E because they still like the king just as much as they did before the vote and he "persuaded" them to change their minds about the war by using influence. Lord B loses 1 relation because while he sort of likes the King, he doesn't love him and the King did overrule the vote. Lord C loses 2 relations because he somewhat dislikes the King though since the king did use "persuasion" to mitigate the damage, the relation loss is not as bad as it would have been otherwise. Lord D hates the king so the fact he got overruled really pisses him off and he takes full relation lose of 10.
Relationship after vote
Lord A: Relation = 53. Lord remains unchanged. 53
Lord B: Relation = 19. Lord loses 1 relation. 18
Lord C: Relation = -10. Lord loses 2 relation -12
Lord D: Relation = -25. Lord loses 10 relation -35
Lord E: Relation = 30. Lord remains unchanged. 30
I will spare everyone the numbers for the last scenario but lets say Lord B at 30 relations instead of 19 and the King used influence. In this cause the use of influence would say the vote entirely into the Kings favor with 2 votes for and 3 against. In this case all 3 who were "Persuaded" would gain 2 Relation for being on the winning side of the vote and Lord C and D would lose a smaller amount of relationship due to the entire Kingdom being against them.
Honestly peace should be like this as well with the King always having the deciding vote. Again if his Kingdom doesn't support peace, there is unrest and he takes a relationship loss with every lord opposed to peace or he can use influence to mitigate this relationship loss but since the King decides he wants peace, it happens, period. However, just because the king wants peace doesn't mean his enemy does so after the vote the enemy ALWAYS should retain the right of refusal. Also if enough of the Kings vassals, not just one or two, that have negative relation with the King, based on the percentage of lords with negative relations there should be a real risk of a full on civil war where multiple lords unite and create their own faction, taking their fiefs with them
That is how all votes should work to be honest. Vote against your vassals too much and piss them off, even while using Influence to midigate the relationship loss, and you run the risk of half or more of your Kingdom just packing up and creating their own rebel faction. This would mean you would have to actually consider what your vassals want and would actually have to decide in their favor at times despite what you would like to do and might even find yourself in a position where your vassals have more power than you because you fear rebellion, but you as the King, ALWAYS retain the right to make the decisions and live with the consequences of that decision.
Note: This still doesn't address the frequency of demands for war which would still screw you in the long run despite having the final say in all decisions but at least you get to act like a King and ACTUALLY have the final say in all things.