Another, related, consideration is that at least in OD&D (where the "1 turn in 6 resting plus 1 turn after combat" rule originated) wandering monster checks are made every turn. Thus these mandatory rest periods add an element of tactical consideration -- wise parties will try to time their rests for when they're behind doors that can be locked or barricaded (thus the importance of iron spikes on the D&D equipment list) so as to not have to rest "out in the open" (in a corridor or chamber) and potentially get caught by wandering monsters.
Also, what happens if the party doesn't take their required rest periods, whether by choice or circumstance? Chainmail (D&D's antecedent game) includes some fatigue rules that aren't exactly compatible but could be pretty easily converted -- IIRC fatigued characters fight as one class lower (which in D&D would equate to a "to hit" penalty of, perhaps, -2), have a penalty on morale (which wouldn't affect PCs but would affect their henchmen and hirelings -- if you don't let them rest they're less likely to follow your orders) and aren't capable of charge or running movement (which is very inconvenient when you want to get away from monsters in a hurry!).
Also, what happens if the party doesn't take their required rest periods, whether by choice or circumstance? Chainmail (D&D's antecedent game) includes some fatigue rules that aren't exactly compatible but could be pretty easily converted -- IIRC fatigued characters fight as one class lower (which in D&D would equate to a "to hit" penalty of, perhaps, -2), have a penalty on morale (which wouldn't affect PCs but would affect their henchmen and hirelings -- if you don't let them rest they're less likely to follow your orders) and aren't capable of charge or running movement (which is very inconvenient when you want to get away from monsters in a hurry!).