An expiration date would be more realistic, but it might be annoying to keep track of since your supplies and money are already decreasing as the days go by. Like, say the player buys supplies from three different locations while travelling, how would they easily be able to tell by looking at the supply number which ones go bad first? Do you add different counters or a viewable list? If so, that could get complicated rather easily. Not to say that it can’t be done, but I feel like it might just add micromanagement without actually adding tension.
The real issue is that food isn’t really important from what we’ve seen so far, outside of mutiny, so there’s only tension related to running out of money. You could circumvent this by adding ways to use supplies as a resource, rather than just having them passively go down. Such as arriving at a city and discovering that the people are starving as a result of raids on the farms. If you don’t share your supplies the militia get weakened even further, running the risk of the city getting razed if you don’t put a stop to the raids. That would also give the player different ways of dealing with a problem: give away supplies so that the militia can fight the raiders for now, deal with the raiders yourself or hope things will work out somehow (or maybe lure in another faction to deal with them?).
Or say that camping is implemented. You could add the option of having the mercenaries dine extravagantly and use way more supplies, but in return get a morale boost at the start of the next combat. Supplies will also naturally become more important once the amount of mercenaries you can have is increased and when non-combatants become an option (since they’ll probably take up supplies as well).
The suggestion of a maximum food limit could add further tension to this, though I’d also add a way to raise the maximum amount of supplies you can bring. Something like letting the player buy carts to bring along.