It's obvious that this claim about ingame time is crucial to the argument. But like Hypersmurf I don't see it. Are the players really worried that their PCs will die of old age before reaching a level high enough to use magic that renders old age irrelevant if they narrate some down time? Certainly, in a sandbox, the world will still be there to be explored in the future.
Time is crucial because if the PCs don't act in time the mage may complete his ritual and become a lich, or the evil duke's bid to overthrow the king and take control of the kingdom may come to fruition, or the drow ambassador might reach and agreement with the local humanoid tribe and combine thier forces when assaulting the local community, or the rival party might find the sword of awsome hidden in the dungeon of death before your party does. In immersive play these things should be meaningful to the PCs, things they don't want to just let happen.