"Subjugate" really means "post war occupation" and "nation building".  Of course, as you point out many games ignore this and gamers are accustomed too "I occupied this city" by simply winning a battle and moving into it.  There is nothing wrong with doing it that way, most games work that way.  But if you are viewing it from the perspective of "Represent Everything", then "subjugating" should be a far more force intensive and time consuming objective.  Time, as you point out, would absolutely also be another factor to include if you were wanting even more detail and "accuracy".

"Subjugate" is something that has actually only rarely actually happened in all of history.  Successfully, anyway.  Germany & Japan are actually two of the only examples in history of an ultimately successful "post war occupation & nation building".  So, in reality, it isn't even actually "a thing", it is an anomaly of history.  There are very few examples in all of history of one nation conquering and absorbing another into a happy new part of their nation or political alliance.

But, again, gamers are used to what you are saying and won't notice or say a thing if you choose to do it that way.  "Represent Everything" is more of a tool to view your design through than a law you must obey.

But actually that would be the "occupy" option (to take over something and now it's a happy normal part of your empire).

The subjugate could be the rulers of a strong empire telling the rulers of a small one: now you do as we say and pay us 20 % or we crush you (or treathen to just kill the leader themselves). Many countries were occupied by germany in ww2. They were not "happy, normal part of the original country", they worked more like unstable, vassal-like territories that needed to be policed, but still contributed to the "mother empire" (heartland germany) with industry, income etc to some degree.

Well, "occupy" actually means that your forces have moved into the area, but it is still "contested".  The enemy is still there.  You've defeated the army, but remnants of the army and civilians will certainly continue the fight against you as a resistance movement.  If you try to produce things in this "province", the people will work as slowly as possible and sabotage production as much as they can.  They might even be blowing up bridges and railways, warehouses, burning fields of crops.  You control them militarily, but that is it.  It has not become a "new production center" of your empire, the place is a complete disaster.

Threatening a nation in the way you are suggesting is "diplomacy".  The way the world works.  That is typical, normal peacetime activity.  To actually carry out the threat would bring you right back to war, post war occupation, nation building.

In our games of the hobbyist era this was often represented by having conquered territory produce far less than home or "core" territory.  Often only 25-50% of production of a home/"core" territory even after you have completely "subjugated" it.  While contested it might produce nothing, or maybe 10%.  This was the most simple way that this was represented in Avalon Hill-like games.