I don’t think its a good idea to implement something like this. To start, the realism of it is questionable since the battles themselves don’t seem to be on a scale that would take hours to resolve. The lengthy amount of time spent on manoeuvring into position, cornering the enemy and choosing the battlefield are already part of the world map, with the battles themselves being about the tactical manoeuvring at relatively close-range. The point at which battle takes place itself would be resolved relatively quickly if it were to actually take place.
Rounds increasing time also creates hypothetical situations where you can win a battle, but come out of it severely starving and broke. That’s not a fair kind of pressure, since there’s no way for you to influence it in battle unless you rush to finish the fight, which is not something you want to encourage in a tactical battle system. Time tension should be a natural occurence in certain battle scenarios (reach the caravan before they kill it), not a constant factor.
You’d also be breaking some intuited abstractions about what is actually happening on the battlefield. If fights actually take hours and potentially days, then it gets really weird that no-one just keels over from exhaustion or just outright starves. That’s currently not a problem, since the pace of the battle is inferred to be short enough that this isn’t an issue, from the kind of actions you take, scale, etc.
Additionally, there’s the effort involved in implementing it since this change would mean that the game would have to simultaneously keep track of what happens on tactical-battle map and everything on the world map, plus making them interact with each other. That would take a lot of time and effort to implement for something that you don’t need.